Quantum Tunneling (Step by Step) Derivation

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Quantum tunneling is a phenomenon where particles pass through a barrier that they seemingly shouldn’t be able to cross based on classical physics. In classical mechanics, a particle requires enough energy to overcome a potential barrier, like a hill. However, in quantum mechanics, particles behave according to the principles of wave-particle duality, meaning they exhibit properties of both waves and particles.

In quantum tunneling, a particle can “tunnel” through a barrier even when its energy is less than the energy required to overcome it. This is due to the probabilistic nature of quantum mechanics, where the particle’s wavefunction extends into and beyond the barrier. The probability of the particle being found on the other side is nonzero, allowing it to appear there, as if it had tunneled through the barrier.

Quantum tunneling is a key process in several important physical phenomena, such as – Nuclear fusion in stars, Electron tunneling in semiconductors, Radioactive decay
Though counterintuitive, quantum tunneling has been experimentally observed and is essential to understanding the quantum behavior of particles at very small scales.

00:00 Introduction
03:19 Quantum Tunneling Derivation

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