Beyond Barriers: Quantum Tunneling

World of Quantum is different from the Classical World and its terminologies, so to under it in better way one need to have great imagination (visualization power) to understand it, curiosity and learning mindset. Hope you have it all of them ticking, if yes the you are great to start your journey with me in Quantum World.

Lets begin.

Imagine you’re walking up to a wall that’s too high to jump over and too solid to break through. In our everyday world, you’d have to find another way around. But in the quantum world, particles sometimes defy these physical barriers—they just pass through. Welcome to the strange world of quantum tunneling, or Spooky world (termed by the great noble scientist : Albert Einstein)

Don't worry, along with this "Dive into the world of Quantum with me, Moksha Shah " article series you will get to know why he termed it as Spooky. Even we discussed about its Spooky nature and Connections in my previous article about the EPR Paradox and Schr?dinger’s Cat. In this article we would understand more about it in depth.

What is Quantum Tunneling?        

In classical physics, particles need enough energy to cross any barrier. But in the quantum world, particles act more like waves than solid objects. This wave behavior allows particles to sometimes “leak” through barriers, even if they don’t have enough energy to overcome them directly.

Lets take a real world example, consider this: every time you use a smartphone or any electronic device, you’re relying on quantum tunneling. It’s the principle behind tunneling diodes and modern transistors, enabling the miniaturization of electronics and the rapid advancement of technology.

In classical physics, a particle with energy E cannot cross a barrier with a potential V.

If E<V

However, in quantum mechanics, the Schr?dinger Equation provides a way to model particle behavior as a wave, which allows for “leakage” through such barriers.

The time-independent Schr?dinger Equation for a particle moving in one dimension is:

Here:

• ? is the reduced Planck’s constant,
• m is the particle’s mass,
• V(x) is the potential energy at position x,
• E is the total energy of the particle,
• ψ(x) is the particle’s wave function, describing its quantum state.

In regions where E<V(x) (inside the barrier), the wave function ψ(x) doesn’t vanish but instead decays exponentially. This decay indicates that there’s a small probability of finding the particle within or beyond the barrier, even though it “shouldn’t” have enough energy to be there. Mathematically, this decaying solution in the barrier region is represented as:

Where κ=√(2m(V?E))/?.

The decay rate κ tells us how quickly the probability drops as the particle moves deeper into the barrier.

The tunneling probability is related to the likelihood of a particle appearing on the other side of the barrier. It’s approximated as:

where d is the barrier width. This probability T drops rapidly with thicker or higher barriers, but it’s never exactly zero, meaning there’s always a chance of tunneling, no matter how unlikely.

The Origins of Quantum Tunneling        

This mind-bending idea emerged from early 20th-century physics as scientists like Erwin Schr?dinger and Max Born developed equations to describe particles as waves.

The mathematical discovery was baffling—even to the scientists themselves—but experiments later confirmed that tunneling was real.

Think of quantum tunneling as a ghost or an invisible man like Mr. India (those who don't know who and what is Mr. India, it's Indian Bollywood movie character who has a power to get invisible because of a cloaking device that would make its user invisible). Someone like a Mr. India or a ghost that can pass through walls in a haunted house. But unlike a that person or ghost, the particle doesn’t vanish and reappear on the other side; it “smears” through the barrier, borrowing energy from its wave-like properties. This behavior is not possible on a large scale, but it’s routine in the subatomic world.

Why Do They Boggle Our Minds?        

Quantum tunneling, like many quantum effects, challenges our common sense and intuition. We’re used to a world where objects follow straightforward rules: walls block us, gravity pulls us down, and things either happen or they don’t. But in the quantum realm, particles act in ways that seem downright magical, breaking through barriers, appearing in multiple places at once, and moving unpredictably.

What’s mind-boggling is that quantum tunneling defies classical laws of physics, showing us that at the smallest scales, the universe isn’t what we’d expect. It reminds us that reality is far richer and stranger than what we see day-to-day—and that’s what makes exploring quantum physics so fascinating.

Why Should You Care?        

Concept of Quantum tunneling may sound like an abstract, “sci-fi” phenomenon, but it’s woven into the fabric of technologies we use every day. Without it, we wouldn’t have the powerful electronics we rely on, from laptops and smartphones to medical imaging equipment. Quantum tunnelling's principles will allow engineers to design ever-smaller transistors, fueling the rapid evolution of computing power and enabling breakthroughs in fields like artificial intelligence, big data, and cloud computing.

And beyond today’s tech, tunneling is unlocking future possibilities. It’s a key player in quantum computing, which could solve complex problems from drug discovery to climate modeling. So, while tunneling might seem distant from our daily lives, its effects—and potential—are closer than we think.

Quantum tunneling holds enormous potential for the future of quantum computing and nanotechnology, as it allows for faster, smaller, and more efficient electronics. It’s also pivotal in nuclear fusion—the very process that powers the sun.

In a Nutshell        

Quantum tunneling allows particles to cross barriers they shouldn’t be able to—kind of like taking a magical shortcut through a wall. It’s strange, but it’s the reason why today’s technology can be as fast, small, and powerful as it is. From smartphones to future quantum computers, tunneling is a hidden hero, helping drive the innovations shaping our world.

Quantum tunneling is a testament to how different the quantum realm is from our everyday experience. It reminds us that at the tiniest scales, nature doesn’t follow the rules we’re familiar with. And perhaps that’s what makes quantum physics so captivating—it invites us to explore and question our understanding of reality.

Stay tuned for the next article, where we’ll dive into how scientists manipulate particles at these quantum scales—ushering in the future of technology through sheer curiosity and ingenuity.

Join Me on This Journey!        

If you find these quantum mysteries intriguing, let’s explore even more! Follow along as I continue diving into the mind-bending world of quantum mechanics in this series. Who knows—maybe the next great discovery is just around the corner.