Tunneling

This last section connects the simulator to wider quantum mechanics. Some ideas, like entanglement and spin, appear directly in quantum information. Others, like tunneling, show how the same formalism explains broader physical phenomena.

In one sentence: Tunneling is the quantum effect where a particle can appear beyond a classically forbidden barrier because its wavefunction extends through the barrier.

Formula

T > 0 even when E < V_{0}

Simple intuition

Classically, not enough energy means no crossing. Quantum mechanically, the wavefunction does not stop sharply at the barrier, so there can still be a small probability of transmission.

Precise explanation

Solving the Schrödinger equation for a barrier gives a wavefunction that decays inside the barrier but is not exactly zero there. Matching the wavefunction across regions leads to a nonzero transmission probability.

Example or analogy

Analogy: imagine sound leaking through a wall even though it is strongly blocked. The analogy captures strong suppression, not absolute zero, but the real calculation comes from the wavefunction and boundary conditions.

Common misconception

Tunneling is not a particle borrowing energy and paying it back later. That is a popular phrase, not the actual explanation.

Why this matters

Tunneling explains real devices and phenomena, including scanning tunneling microscopes, alpha decay, and parts of semiconductor physics.

Self-check

• Why is tunneling allowed even when the classical energy is too low?
• What quantity stays small but nonzero inside the barrier?

↗ MIT OCW 8.04: lecture notes ↗ Griffiths and Schroeter, Introduction to Quantum Mechanics

Entanglement and Other Quantum Effects

Spin

Entanglement and Other Quantum Effects

Phase kickback and the road to algorithms

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Entanglement and Other Quantum Effects

Tunneling

In one sentence: Tunneling is the quantum effect where a particle can appear beyond a classically forbidden barrier because its wavefunction extends through the barrier.

Formula

T > 0 even when E < V_{0}

Simple intuition

Classically, not enough energy means no crossing. Quantum mechanically, the wavefunction does not stop sharply at the barrier, so there can still be a small probability of transmission.

Precise explanation

Example or analogy

Common misconception

Tunneling is not a particle borrowing energy and paying it back later. That is a popular phrase, not the actual explanation.

Why this matters

Tunneling explains real devices and phenomena, including scanning tunneling microscopes, alpha decay, and parts of semiconductor physics.

Self-check

• Why is tunneling allowed even when the classical energy is too low?
• What quantity stays small but nonzero inside the barrier?

↗ MIT OCW 8.04: lecture notes ↗ Griffiths and Schroeter, Introduction to Quantum Mechanics

Entanglement and Other Quantum Effects

Spin

Entanglement and Other Quantum Effects

Phase kickback and the road to algorithms