Quantum Particle Field: Wavefunction Tunneling Lab (2D) |…

What Wavefunction Tunneling Is

Wavefunction tunneling is a phenomenon in quantum mechanics where particles can pass through potential barriers even when their energy is less than the barrier height. This occurs due to the probabilistic nature of wavefunctions, which allows for non-zero probability amplitudes within classically forbidden regions.

In this 2D simulation, you observe how a Gaussian wavepacket interacts with and tunnels through a controllable potential barrier, illustrating key quantum mechanical principles.

Why It Happens

Wavefunction tunneling happens because the wavefunction of a particle extends beyond the classical turning points where its kinetic energy is less than the potential energy. This extension allows for a non-zero probability density in classically forbidden regions, enabling particles to have a finite probability of appearing on the other side of the barrier.

The phenomenon can be described by the time-dependent Schrödinger equation, which governs how wavefunctions evolve over time and interact with potentials.

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Real-World Applications

Wavefunction tunneling has numerous applications in various fields. In electronics, it is crucial for the operation of tunnel diodes and quantum dots. It also plays a significant role in nuclear physics, where alpha particles can tunnel through nuclear barriers.

In chemistry, understanding tunneling helps explain certain chemical reactions that proceed via pathways forbidden to classical particles.

Key Concepts in the Simulation

The simulation allows you to manipulate several parameters such as the wavepacket's momentum and Gaussian width, which affect its behavior. The potential barrier height can be adjusted to observe how it influences tunneling probabilities. Additionally, the live transmission probability and position spread provide insights into the quantum nature of particles.

The measurement/collapse button demonstrates a real projective measurement, collapsing the wavefunction into a narrow packet at a sampled position from the |ψ|² distribution.

Frequently asked questions

What is the time-dependent Schrödinger equation?

The time-dependent Schrödinger equation describes how the quantum state of a physical system changes with time. It is central to non-relativistic quantum mechanics and governs the evolution of wavefunctions.

How does tunneling probability change with barrier height?

As the potential barrier height increases, the transmission probability decreases exponentially due to the decrease in the region where the particle's energy can be positive relative to the barrier height.

What is a Gaussian wavepacket?

A Gaussian wavepacket is a localized wavefunction that resembles a bell curve. It represents a particle with a well-defined momentum and position, making it useful for studying tunneling phenomena.

Why does the measurement/collapse button matter in quantum mechanics?

The measurement/collapse button illustrates the collapse of the wavefunction into a definite state upon measurement. This demonstrates the probabilistic nature of quantum states and the non-deterministic outcomes of measurements.

Try it live

Everything above runs in your browser — open Quantum Particle Field: Wavefunction Tunneling Lab (2D) and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

▶ Open Quantum Particle Field: Wavefunction Tunneling Lab (2D) simulation