THE BUSINESS PLAN
We all need a place to start. In fact this is inevitable. We all have to start somewhere. Some of the most powerful tools, are the most basic ones. Think about a calendar. And then add a calculator. Grab a basic note pad, some pens and pencils, and maybe some stick it notes, or cue cards. Then follow these simple, back to the basics steps.
Having clearly defined goals, daily, weekly and monthly/ quarterly are as essential to our success, as the journals we keep. We need to add interactivity to all of our dream boards. I reached out to Wiki, to see what I could find to help us.
A.)
A?business plan?is a formal written document containing the goals of a?business , the methods for attaining those goals, and the time-frame for the achievement of the goals. It also describes the nature of the business, background information on the?organization , the organization's financial projections, and the?strategies ?it intends to implement to achieve the stated targets. In its entirety, this document serves as a road-map (a?plan ) that provides direction to the business.[1] [2]
Written business plans are often required to obtain a?bank loan ?or other kind of?financing . Templates?[3] ?and guides, such as the ones offered in the United States by the?Small Business Administration [4] ?can be used to facilitate producing a business plan.
Audience
Business plans may be internally or externally focused. Externally-focused plans draft goals that are important to outside stakeholders, particularly financial stakeholders. These plans typically have detailed information about the organization or the team making effort to reach its goals. With for-profit entities, external stakeholders include investors and customers,[5] ?for non-profits, external stakeholders refer to donors and clients,[6] ?for government agencies, external stakeholders are the tax-payers, higher-level government agencies, and international lending bodies such as the?International Monetary Fund , the?World Bank , various economic agencies of the?United Nations , and?development banks .
Internally-focused business plans target intermediate goals required to reach the external goals. They may cover the development of a new product, a new service, a new IT system, a restructuring of finance, the refurbishing of a factory or the restructuring of an organization. An internally-focused business plan is often developed in conjunction with a?balanced scorecard ?or?OGSM ?or a list of critical success factors. This allows the success of the plan to be measured using non-financial measures.
Business plans that identify and target internal goals, but provide only general guidance on how they will be met are called?strategic plans .
Operational plans describe the goals of an internal organization, working group or department.[7] ?Project plans, sometimes known as project frameworks, describe the goals of a particular project. They may also address the project's place within the organization's larger strategic goals.[8]
Content
Business plans are?decision-making tools . The content and format of the business plan are determined by the goals and audience. For example, a business plan for a non-profit might discuss the fit between the business plan and the organization's mission. Banks are quite concerned about defaults, so a business plan for a bank loan will build a convincing case for the organization's ability to repay the loan.?Venture capitalists ?are primarily concerned about initial investment, feasibility, and exit valuation. A business plan for a project requiring equity financing will need to explain why current resources, upcoming growth opportunities, and?sustainable competitive advantage ?will lead to a high exit valuation.[9]
Preparing a business plan draws on a wide range of knowledge from many different business disciplines:?finance , human resource management,?intellectual property ?management,?supply chain management , operations management, and?marketing , among others.[10] ?It can be helpful to view the business plan as a collection of sub-plans, one for each of the main business disciplines.[11]
"... a good business plan can help to make a good business credible, understandable, and attractive to someone who is unfamiliar with the business. Writing a good business plan can't guarantee success, but it can go a long way toward reducing the odds of failure."[11]
B.)
The format of a business plan depends on its presentation context. It is common for businesses, especially start-ups, to have three or four formats for the same business plan.
An "elevator pitch " is a short summary of the plan's executive summary. This is often used as a teaser to awaken the interest of potential investors, customers, or strategic partners. It is called an elevator pitch as it is supposed to be content that can be explained to someone else quickly in an elevator. The elevator pitch should be between 30 and 60 seconds.[12]
A?pitch deck ?is a slide show and oral presentation that is meant to trigger discussion and interest potential investors in reading the written presentation. The content of the presentation is usually limited to the executive summary and a few key graphs showing financial trends and key decision-making benchmarks. If a new product is being proposed and time permits, a demonstration of the product may be included.[13]
A written presentation for external stakeholders is a detailed, well written, and pleasingly formatted plan targeted at external stakeholders.
An internal operational plan is a detailed plan describing planning details that are needed by management but may not be of interest to external stakeholders. Such plans have a somewhat higher degree of candor and informality than the version targeted at external stakeholders and others.
Business plans for start-ups
Typical structure for a business plan for a start-up venture?[14]
Typical questions addressed by a business plan for a start-up venture?[15]
C.)
You. Your vision and your dreams are required. "Aint no half stepping".
2015 YZF-R1
Yamaha R1M at 2015 Tokyo Motor Show
At the centennial?EICMA ?motorcycle show, Yamaha officially unveiled a new generation of R1,[14] ?similar to the contemporary YZR M1. Yamaha claims a wet weight of 199?kg (439?lb).[15] ?Engine changes include a decreased?bore-to-stroke ratio , a larger?airbox , a finger-follower valve system, and fracture split titanium?conrods .[16] ?Magnesium wheels are standard, and information is presented to the rider through a user-customizable thin-film display.[16]
The new bike has an electronics package that includes a sophisticated Traction Control System (TCS), a Slide Control System (SCS), an anti-wheelie Lift Control System (LIF), linked?antilock brakes , a?Launch Control ?System (LCS), a?Quick Shift ?System (QSS), and selectable power modes. The Slide Control System on the R1 is the first on a production motorcycle.[16] [17] ?Information is fed to the bike through a six-axis?inertial measurement unit ?and other sensors over 100 times a second.[17] ?Power delivery is tapered through throttle valve manipulation and ignition and fuel cuts.[18]
A second higher-spec, limited production model called the R1M is also produced, and is differentiated from the standard model by having more expensive components, such as electronic semi-active ?hlins suspension, carbon fiber bodywork, Yamaha's Communication Control Unit (CCU), a Y-TRAC data logging system, and grippier?Bridgestone ?tires with a larger rear 200/55 size.
At EICMA 2017 Yahama presented the next generation of R1 and R1M. They have a better Quick Shift System, an updated Lift (wheelie) Control System and fulfill Euro 4 requirements. The R1M got a new ?hlins Electronic Racing Suspension.[3] ?In 2019 next new models started.[4]
I went online to look at these to add to my collection. I found some base models for $17,000.00 to $18,000.00 give and take. That was cool. With inflation, I guessed they would dance at this price range. Then, I looked at a Ducati Panigale V2, for less than $2,000.00 more and I said. "I am bugging". The Ducati it is.
In both life and business, sometimes we settle for only, what is known or readily available. But our breakthrough, may be one small, baby step away. The prestige of having a hand built bike, is far greater than any other advantages, that the other competitors in this segment; can provide. In this case. Legacy and long term value is more to me, than anything else.
Revising the business plan
Cost overruns and revenue shortfalls
Cost and?revenue ?estimates are central to any business plan for deciding the viability of the planned venture. But costs are often underestimated and revenues overestimated resulting in later cost overruns, revenue shortfalls, and possibly non-viability. During the?dot-com bubble ?1997-2001 this was a problem for many technology start-ups.?Reference class forecasting ?has been developed to reduce the risks of cost overruns and revenue shortfalls and thus generate more accurate business plans.
Disclosure requirements
An externally targeted business plan should list all legal concerns and financial liabilities that might negatively affect investors. Depending on the number of funds being raised and the audience to whom the plan is presented, failure to do this may have severe legal consequences.
Limitations on content and audience[edit ]
Non-disclosure agreements ?(NDAs) with third parties,?non-compete agreements , conflicts of interest, privacy concerns, and the protection of one's?trade secrets ?may severely limit the audience to which one might show the business plan. Alternatively, they may require each party to receive the business plan to sign a contract accepting special clauses and conditions.
This situation is complicated by the fact that many venture capitalists will refuse to sign an?NDA ?before looking at a business plan, lest it put them in the untenable position of looking at two independently developed look-alike business plans, both claiming originality. In such situations, one may need to develop two versions of the business plan: a stripped-down plan that can be used to develop a relationship and a detailed plan that is only shown when investors have sufficient interest and trust to sign a Non-disclosure agreement.
The?Ducati Panigale V2?is a 955?cc (58.3 cu in)?V-twin engine ?sport bike manufactured by?Ducati ?as the successor to the?Panigale 959 . The motorcycle is named after the manufacturing district of?Borgo Panigale . It was announced in 2019 for the 2020 model year. Chassis is a very similar?monocoque ?with stressed-member engine; the engine bore and stroke remained the same; some re-engineering resulted in a 5 horsepower (3.7?kW) increase and?Euro 5 ?emissions compliance.[1]
The Navy Seals have this famous saying. "Who's going to carry the boats"? We must scream, as loud as we can. "I'm gonna carry the boats"!. When it comes to our lives and our careers. When it comes to our exclusive brands, products, or services. In all of the things that we do, when it comes to our pursuit of happiness and our success.
The?United States Navy Sea, Air, and Land?(SEAL)?Teams, commonly known as?Navy SEALs, are the?U.S. Navy's ?primary?special operations force ?and a component of the?Naval Special Warfare Command . Among the SEALs' main functions are conducting small-unit special operation missions in maritime, jungle, urban, arctic, mountainous, and desert environments. SEALs are typically ordered to capture or to kill high level targets, or to gather intelligence behind enemy lines.[7] ?SEAL team personnel are hand selected, highly trained, and possess a high degree of proficiency in direct action (DA), and special reconnaissance (SR), among other tasks like sabotage, demolition, intelligence gathering, and hydro-graphic reconnaissance, training, and advising friendly militaries or other forces.?[8]
Depending on the availability of platforms, threat level, and environment, different methods can be used for the insertion and extraction of SEALs into a target location. This could include nuclear-powered cruise missile submarines equipped with dry deck shelters, SDV submarines, surface vessels, surface swimming, or other vehicles
All active SEALs are members of the U.S. Navy.[12] ?The?CIA 's highly secretive and elite?Special Operations Group (SOG) ?recruits operators from SEAL Teams,[13] ?with joint operations going back to the?MACV-SOG ?during the?Vietnam War .[14] ?This cooperation still exists today, as evidenced by?military operations ?in?Iraq ?and?Afghanistan .[15] [16]
History
Origins
Although not formally founded until 1962, the modern-day U.S. Navy SEALs trace their roots to?World War II .[7] ?The United States Military recognized the need for the?covert ?reconnaissance ?of?landing beaches ?and?coastal defenses . As a result, the joint Army, Marine Corps, and Navy?Amphibious Scout and Raider ?School was established in 1942 at?Fort Pierce, Florida .[11] ?The Scouts and Raiders were formed in September of that year, just nine months after the?attack on Pearl Harbor , from the?Observer Group , a joint U.S. Army-Marine-Navy unit.Traditionally business plans have been highly confidential and quite limited in the audience. The business plan itself is generally regarded as a secret.
An open business plan is a business plan with an unlimited audience. The business plan is typically web published and made available to all.
In the free software and open source business model, trade secrets,?copyright ?and patents can no longer be used as effective locking mechanisms to provide sustainable advantages to a particular business and therefore a secret business plan is less relevant in those models
领英推荐
We cannot go to the three point line to get ready, or prepare. We cannot go to the foul line to think about all of the things that need to be done. Look how Denver won the NBA Championship title by only 4 points. We cannot afford to lose anymore. Enough is enough. Who is going to stop us? I fear nothing but failure.
Psychology?is the?scientific ?study of?mind ?and?behavior ?in humans and non-humans. Psychology includes the study of?conscious ?and?unconscious ?phenomena, including?feelings ?and?thoughts . It is an academic discipline of immense scope, crossing the boundaries between the?natural ?and?social sciences . Psychologists seek an understanding of the?emergent ?properties of?brains , linking the discipline to?neuroscience . As social scientists, psychologists aim to understand the behavior of individuals and groups.[1] [2] ?Ψ?(psi) , the first?letter ?of the Greek word?psyche?from which the term psychology is derived (see below), is commonly associated with the science.
A professional practitioner or researcher involved in the discipline is called a?psychologist . Some psychologists can also be classified as?behavioral ?or?cognitive scientists . Some psychologists attempt to understand the role of mental functions in individual and?social behavior . Others explore the?physiological ?and?neurobiological ?processes that underlie cognitive functions and behaviors.
Psychologists are involved in research on?perception ,?cognition ,?attention ,?emotion ,?intelligence ,?subjective experiences ,?motivation ,?brain functioning , and?personality . Psychologists' interests extend to?interpersonal relationships ,?psychological resilience ,?family resilience , and other areas within?social psychology . They also consider the unconscious mind.[3] ?Research psychologists employ?empirical methods ?to infer?causal ?and?correlational ?relationships between psychosocial?variables . Some, but not all,?clinical ?and?counseling ?psychologists rely on?symbolic interpretation .
While psychological knowledge is often applied to the assessment and treatment of mental health problems, it is also directed towards understanding and solving problems in several spheres of human activity. By many accounts, psychology ultimately aims to benefit society.[4] [5] [6] ?Many psychologists are involved in some kind of therapeutic role, practicing?psychotherapy ?in clinical, counseling, or?school ?settings. Other psychologists conduct scientific research on a wide range of topics related to mental processes and behavior. Typically the latter group of psychologists work in academic settings (e.g., universities, medical schools, or hospitals). Another group of psychologists is employed in?industrial and organizational ?settings.[7] ?Yet others are involved in work on?human development , aging,?sports , health,?forensic science ,?education , and the?media .
The time to be successful is finally upon us. There is no time to lose. There are no resources to waste. Time is everything. Lets eliminate complexities, by simplification tactics. Lets all move at the pace of business. We are the driving engines/ force and we are the brakes. We get to decide. Lets all decide on all of the commitments of success.
Fundraising is the primary purpose of many business plans since they are related to the inherent probable success/failure of the company risk.
Not for-profit businesses
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The business goals may be defined both for?non-profit ?or for-profit organizations. For-profit business plans typically focus on financial goals, such as profit or creation of wealth. Non-profit, as well as government agency business plans tend to focus on the "organizational mission" which is the basis for their governmental status or their non-profit, tax-exempt status, respectively—although non-profits may also focus on optimizing revenue.
The primary difference between profit and non-profit organizations is that "for-profit" organizations look to maximize wealth versus non-profit organizations, which look to provide a greater good to society. In non-profit organizations, creative tensions may develop in the effort to balance mission with "margin" (or revenue).
Satires
The business plan is the subject of many satires. Satires are used both to express cynicism about business plans and as an educational tool to improve the quality of business plans. For example,
Read all of your old business books, or go back online and re take those old classes. Re visit your written notes, in highlighter; inside your old libraries. You may learn some new elements, you may have overlooked. Bring those old books from you garage, back into your offices. When faced with a challenge, re process that data. Apply that knowledge within, in real time, to any and all factors of your business today.
Etymology and definitions
The word?psychology ?derives from the Greek word?psyche , for spirit or?soul . The latter part of the word "psychology" derives from -λογ?α?-logia , which refers to "study" or "research".[8] ?The word psychology was first used in the Renaissance.[9] ?In its?Latin ?form "psychiologia", it was first employed by the?Croatian ?humanist ?and?Latinist ?Marko Maruli? ?in his book?Psichiologia de ratione animae humanae ?(Psychology, on the Nature of the Human Soul) in the decade 1510-1520[9] [10] ?The earliest known reference to the word?psychology?in English was by?Steven Blankaart ?in 1694 in?The Physical Dictionary. The dictionary refers to "Anatomy, which treats the Body, and Psychology, which treats of the Soul."[11]
In 1890,?William James ?defined?psychology?as "the science of mental life, both of its phenomena and their conditions."[12] ?This definition enjoyed widespread currency for decades. However, this meaning was contested, notably by radical?behaviorists ?such as?John B. Watson , who in 1913 asserted that the discipline is a "natural science", the theoretical goal of which "is the prediction and control of behavior."[13] ?Since James defined "psychology", the term more strongly implicates scientific?experimentation .[14] [13] ?Folk psychology ?refers to?ordinary people 's, as contrasted with psychology professionals', understanding of the mental states and behaviors of people.[15]
Quantum mechanics?is a fundamental?theory ?in?physics ?that provides a description of the physical properties of?nature ?at the scale of?atoms ?and?subatomic particles .[2] : 1.1 ?It is the foundation of all quantum physics including?quantum chemistry ,?quantum field theory ,?quantum technology , and?quantum information science .
Classical physics , the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic ) scale, but is not sufficient for describing them at small (atomic and?subatomic ) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.[3]
Quantum mechanics differs from classical physics in that?energy ,?momentum ,?angular momentum , and other quantities of a?bound ?system are restricted to?discrete values ?(quantization ); objects have characteristics of both?particles ?and?waves ?(wave–particle duality ); and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the?uncertainty principle ).
Quantum mechanics?arose gradually ?from theories to explain observations that could not be reconciled with classical physics, such as?Max Planck 's solution in 1900 to the?black-body radiation ?problem, and the correspondence between energy and frequency in?Albert Einstein 's?1905 paper , which explained the?photoelectric effect . These early attempts to understand microscopic phenomena, now known as the "old quantum theory ", led to the full development of quantum mechanics in the mid-1920s by?Niels Bohr ,?Erwin Schr?dinger ,?Werner Heisenberg ,?Max Born ,?Paul Dirac ?and others. The modern theory is formulated in various?specially developed mathematical formalisms . In one of them, a mathematical entity called the?wave function ?provides information, in the form of?probability amplitudes , about what measurements of a particle's energy, momentum, and other physical properties may yield.
Overview and fundamental concepts
Quantum mechanics allows the calculation of properties and behaviour of physical systems. It is typically applied to microscopic systems: molecules, atoms and sub-atomic particles. It has been demonstrated to hold for complex molecules with thousands of atoms,[4] ?but its application to human beings raises philosophical problems, such as?Wigner's friend , and its application to the universe as a whole remains speculative.[5] ?Predictions of quantum mechanics have been verified experimentally to an extremely high degree of?accuracy .[note 1]
A fundamental feature of the theory is that it usually cannot predict with certainty what will happen, but only give probabilities. Mathematically, a probability is found by taking the square of the absolute value of a?complex number , known as a probability amplitude. This is known as the?Born rule , named after physicist?Max Born . For example, a quantum particle like an?electron ?can be described by a?wave function , which associates to each point in space a probability amplitude. Applying the Born rule to these amplitudes gives a?probability density function ?for the position that the electron will be found to have when an experiment is performed to measure it. This is the best the theory can do; it cannot say for certain where the electron will be found. The?Schr?dinger equation ?relates the collection of probability amplitudes that pertain to one moment of time to the collection of probability amplitudes that pertain to another.
One consequence of the mathematical rules of quantum mechanics is a tradeoff in predictability between different measurable quantities. The most famous form of this?uncertainty principle ?says that no matter how a quantum particle is prepared or how carefully experiments upon it are arranged, it is impossible to have a precise prediction for a measurement of its position and also at the same time for a measurement of its?momentum .
Another consequence of the mathematical rules of quantum mechanics is the phenomenon of?quantum interference , which is often illustrated with the?double-slit experiment . In the basic version of this experiment, a?coherent light source , such as a?laser ?beam, illuminates a plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate.[6] : 102–111 [2] : 1.1–1.8 ?The wave nature of light causes the light waves passing through the two slits to?interfere , producing bright and dark bands on the screen – a result that would not be expected if light consisted of classical particles.[6] ?However, the light is always found to be absorbed at the screen at discrete points, as individual particles rather than waves; the interference pattern appears via the varying density of these particle hits on the screen. Furthermore, versions of the experiment that include detectors at the slits find that each detected?photon ?passes through one slit (as would a classical particle), and not through both slits (as would a wave).[6] : 109 [7] [8] ?However,?such experiments ?demonstrate that particles do not form the interference pattern if one detects which slit they pass through. Other atomic-scale entities, such as?electrons , are found to exhibit the same behavior when fired towards a double slit.[2] ?This behavior is known as?wave–particle duality .
Another counter-intuitive phenomenon predicted by quantum mechanics is?quantum tunnelling : a particle that goes up against a?potential barrier ?can cross it, even if its kinetic energy is smaller than the maximum of the potential.[9] ?In classical mechanics this particle would be trapped. Quantum tunnelling has several important consequences, enabling?radioactive decay ,?nuclear fusion ?in stars, and applications such as?scanning tunnelling microscopy ?and the?tunnel diode .[10]
When quantum systems interact, the result can be the creation of?quantum entanglement : their properties become so intertwined that a description of the whole solely in terms of the individual parts is no longer possible. Erwin Schr?dinger called entanglement "...the?characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought".[11] ?Quantum entanglement enables the counter-intuitive properties of?quantum pseudo-telepathy , and can be a valuable resource in communication protocols, such as?quantum key distribution ?and?superdense coding .[12] ?Contrary to popular misconception, entanglement does not allow sending signals?faster than light , as demonstrated by the?no-communication theorem .[12]
Another possibility opened by entanglement is testing for "hidden variables ", hypothetical properties more fundamental than the quantities addressed in quantum theory itself, knowledge of which would allow more exact predictions than quantum theory can provide. A collection of results, most significantly?Bell's theorem , have demonstrated that broad classes of such hidden-variable theories are in fact incompatible with quantum physics. According to Bell's theorem, if nature actually operates in accord with any theory of?local?hidden variables, then the results of a?Bell test ?will be constrained in a particular, quantifiable way. Many Bell tests have been performed, using entangled particles, and they have shown results incompatible with the constraints imposed by local hidden variables.[13] [14]
It is not possible to present these concepts in more than a superficial way without introducing the actual mathematics involved; understanding quantum mechanics requires not only manipulating complex numbers, but also?linear algebra ,?differential equations ,?group theory , and other more advanced subjects.[note 2] ?Accordingly, this article will present a mathematical formulation of quantum mechanics and survey its application to some useful and oft-studied examples.
The?mathematical formulations of quantum mechanics?are those?mathematical formalisms ?that permit a rigorous description of?quantum mechanics . This mathematical formalism uses mainly a part of?functional analysis , especially?Hilbert spaces , which are a kind of?linear space . Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional?Hilbert spaces ?(L2?space ?mainly), and?operators ?on these spaces. In brief, values of physical?observables ?such as?energy ?and?momentum ?were no longer considered as values of?functions ?on?phase space , but as?eigenvalues ; more precisely as?spectral values ?of linear?operators ?in Hilbert space.[1]
These formulations of quantum mechanics continue to be used today. At the heart of the description are ideas of?quantum state ?and?quantum observables, which are radically different from those used in previous?models ?of physical reality. While the mathematics permits calculation of many quantities that can be measured experimentally, there is a definite theoretical limit to values that can be simultaneously measured. This limitation was first elucidated by?Heisenberg ?through a?thought experiment , and is represented mathematically in the new formalism by the?non-commutativity ?of operators representing quantum observables.
Prior to the development of quantum mechanics as a separate?theory , the mathematics used in physics consisted mainly of formal?mathematical analysis , beginning with?calculus , and increasing in complexity up to?differential geometry ?and?partial differential equations .?Probability theory ?was used in?statistical mechanics . Geometric intuition played a strong role in the first two and, accordingly,?theories of relativity ?were formulated entirely in terms of differential geometric concepts. The phenomenology of quantum physics arose roughly between 1895 and 1915, and for the 10 to 15 years before the development of quantum mechanics (around 1925) physicists continued to think of quantum theory within the confines of what is now called?classical physics , and in particular within the same mathematical structures. The most sophisticated example of this is the?Sommerfeld–Wilson–Ishiwara quantization ?rule, which was formulated entirely on the classical?phase space .
In the 1890s,?Planck ?was able to derive the?blackbody spectrum , which was later used to avoid the classical?ultraviolet catastrophe ?by making the unorthodox assumption that, in the interaction of?electromagnetic radiation ?with?matter , energy could only be exchanged in discrete units which he called?quanta . Planck postulated a direct proportionality between the frequency of radiation and the quantum of energy at that frequency. The proportionality constant,?h, is now called?Planck's constant ?in his honor.
In 1905,?Einstein ?explained certain features of the?photoelectric effect ?by assuming that Planck's energy quanta were actual particles, which were later dubbed?photons .
All of these developments were?phenomenological ?and challenged the theoretical physics of the time.?Bohr and Sommerfeld ?went on to modify?classical mechanics ?in an attempt to deduce the?Bohr model ?from first principles. They proposed that, of all closed classical orbits traced by a mechanical system in its?phase space , only the ones that enclosed an area which was a multiple of Planck's constant were actually allowed. The most sophisticated version of this formalism was the so-called?Sommerfeld–Wilson–Ishiwara quantization . Although the Bohr model of the hydrogen atom could be explained in this way, the spectrum of the helium atom (classically an unsolvable?3-body problem ) could not be predicted. The mathematical status of quantum theory remained uncertain for some time.
In 1923,?de Broglie ?proposed that?wave–particle duality ?applied not only to photons but to electrons and every other physical system.
The situation changed rapidly in the years 1925–1930, when working mathematical foundations were found through the groundbreaking work of?Erwin Schr?dinger ,?Werner Heisenberg ,?Max Born ,?Pascual Jordan , and the foundational work of?John von Neumann ,?Hermann Weyl ?and?Paul Dirac , and it became possible to unify several different approaches in terms of a fresh set of ideas. The physical interpretation of the theory was also clarified in these years after?Werner Heisenberg ?discovered the uncertainty relations and?Niels Bohr ?introduced the idea of?complementarity .
The "new quantum theory"[edit ]
Werner Heisenberg 's?matrix mechanics ?was the first successful attempt at replicating the observed quantization of?atomic spectra . Later in the same year, Schr?dinger created his?wave mechanics . Schr?dinger's formalism was considered easier to understand, visualize and calculate as it led to?differential equations , which physicists were already familiar with solving. Within a year, it was shown that the two theories were equivalent.
Schr?dinger himself initially did not understand the fundamental probabilistic nature of quantum mechanics, as he thought that the?absolute square ?of the wave function of an?electron ?should be interpreted as the?charge density ?of an object smeared out over an extended, possibly infinite, volume of space. It was?Max Born ?who introduced the interpretation of the?absolute square ?of the wave function as the probability distribution of the position of a?pointlike?object . Born's idea was soon taken over by Niels Bohr in Copenhagen who then became the "father" of the?Copenhagen interpretation ?of quantum mechanics. Schr?dinger's?wave function ?can be seen to be closely related to the classical?Hamilton–Jacobi equation . The correspondence to classical mechanics was even more explicit, although somewhat more formal, in Heisenberg's matrix mechanics. In his PhD thesis project,?Paul Dirac [2] ?discovered that the equation for the operators in the?Heisenberg representation , as it is now called, closely translates to classical equations for the dynamics of certain quantities in the Hamiltonian formalism of classical mechanics, when one expresses them through?Poisson brackets , a procedure now known as?canonical quantization .
To be more precise, already before Schr?dinger, the young postdoctoral fellow?Werner Heisenberg ?invented his?matrix mechanics , which was the first correct quantum mechanics–– the essential breakthrough. Heisenberg's?matrix mechanics ?formulation was based on algebras of infinite matrices, a very radical formulation in light of the mathematics of classical physics, although he started from the index-terminology of the experimentalists of that time, not even aware that his "index-schemes" were matrices, as Born soon pointed out to him. In fact, in these early years,?linear algebra ?was not generally popular with physicists in its present form.
Although Schr?dinger himself after a year proved the equivalence of his wave-mechanics and Heisenberg's matrix mechanics, the reconciliation of the two approaches and their modern abstraction as motions in Hilbert space is generally attributed to?Paul Dirac , who wrote a lucid account in his 1930 classic?The Principles of Quantum Mechanics . He is the third, and possibly most important, pillar of that field (he soon was the only one to have discovered a relativistic generalization of the theory). In his above-mentioned account, he introduced the?bra–ket notation , together with an abstract formulation in terms of the?Hilbert space ?used in?functional analysis ; he showed that Schr?dinger's and Heisenberg's approaches were two different representations of the same theory, and found a third, most general one, which represented the dynamics of the system. His work was particularly fruitful in many types of generalizations of the field.
The first complete mathematical formulation of this approach, known as the?Dirac–von Neumann axioms , is generally credited to?John von Neumann 's 1932 book?Mathematical Foundations of Quantum Mechanics , although?Hermann Weyl ?had already referred to Hilbert spaces (which he called?unitary spaces) in his 1927 classic paper and book. It was developed in parallel with a new approach to the mathematical?spectral theory ?based on?linear operators ?rather than the?quadratic forms ?that were?David Hilbert 's approach a generation earlier. Though theories of quantum mechanics continue to evolve to this day, there is a basic framework for the mathematical formulation of quantum mechanics which underlies most approaches and can be traced back to the mathematical work of?John von Neumann . In other words, discussions about?interpretation?of the theory , and extensions to it, are now mostly conducted on the basis of shared assumptions about the mathematical foundations.
All these blue links work. These are all from Wiki. Everything that I am studying for my business ventures, I share with you all in hopes that it may help you. I gave you apps, books, audibles, audio books, plus some insights. Everything is formatted and sequenced here for all of us. We can allways, like subscribe and share with our entire staff and teams. It is forever archived here on the cloud.
We can all go back and simply start over by re-reading. The goal is for each and every one of us to add our own flair to things, and spice it up. We all bring our own unique experiences to the mix. We can read it out loud when recording our journals, and write anything down. We can revisit, any segment and apply it to our clearly defined goals.
These are footnote guides, designed to be step by step for all entrepreneurship levels. No product, brand, service, trade or field is too small or too complex. We are all here to learn from each other. I love tech. This is how I implement it in real time.
I had to look further and beyond my wildest dreams in order to achieve success. And guess what? You all can too. I released 3 albums yesterday. And one compilation album, combining them all together. A podcast and a new magazine article. Now. Back to the basics. Some emails. Some phone calls and some confirmations for several business meetings. Another day in our pursuit of happiness.
This is how. Lmao. I love you all.