Quantum Tunneling: Wavepacket vs. Potential Barrier (2D) |…

What Quantum Tunneling Is

Quantum tunneling is a phenomenon where particles can pass through potential barriers that they classically should not be able to cross. This occurs due to the wave-like nature of quantum particles, allowing them to exist in regions with negative probability amplitudes on the other side of the barrier.

The concept was first introduced by Gurney and Condon in 1928 and has since been crucial for understanding phenomena such as alpha decay, electron microscopy, and semiconductor devices.

How It Works

In the simulation, a Gaussian wavepacket is used to model the particle's behavior. When this wavepacket encounters a rectangular potential barrier, it spreads out due to its wave-like properties. Some of the probability density of the wavepacket can be found on the other side of the barrier, even if the classical energy of the particle is lower than the height of the barrier.

The simulation numerically solves the Schrodinger equation for this system and compares the transmission coefficient (the fraction of particles that tunnel through) with the exact formula derived from quantum mechanics.

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Why It Matters

Quantum tunneling is essential in many technological applications, such as scanning tunneling microscopes used to image surfaces at atomic resolution and tunnel diodes that operate based on this principle.

Understanding quantum tunneling also aids in the development of new materials and devices, including transistors and quantum computers.

Real-World Examples

In semiconductor physics, tunnel junctions are used to create diodes that can operate at very low voltages. These devices are crucial for the development of solid-state lighting and energy-efficient electronics.

Another example is in nuclear fusion research, where quantum tunneling plays a significant role in enabling fusion reactions to occur even when the reactants do not have sufficient kinetic energy.

Frequently asked questions

How does quantum tunneling differ from classical mechanics?

In classical mechanics, particles cannot pass through potential barriers if their energy is lower than the barrier's height. Quantum mechanics allows for a non-zero probability of particles being found on the other side of such barriers due to wave-like properties and superposition.

What are some practical applications of quantum tunneling?

Quantum tunneling is used in various technologies, including scanning tunneling microscopes for imaging surfaces at atomic scale, tunnel diodes for low-voltage electronics, and semiconductor devices like transistors that rely on the phenomenon to function.

Can quantum tunneling be observed with macroscopic objects?

Quantum tunneling is typically observable only at microscopic scales due to the small energy differences involved. However, it can be demonstrated in experiments using electrons or other subatomic particles.

Is quantum tunneling a violation of conservation of energy?

No, quantum tunneling does not violate conservation of energy because the probability amplitudes are complex numbers and the total probability is conserved. The wavefunction's modulus squared gives the probability density, which integrates to one.

Try it live

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

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