Quantum Mechanics Visualizations

Quantum Mechanics Visualizations

Particle in a Box Wave Function Superposition Quantum Harmonic Oscillator

Particle in a Box Controls

Energy Level (n): 1

Box Width (L): 2.0 nm

Particle Mass (m): 1 × m_e (electron mass)

Wave Function Superposition Controls

First State (n₁): 1

Second State (n₂): 2

Relative Phase: 0.0 rad

Time Evolution: 0%

Harmonic Oscillator Controls

Energy Level (n): 0

Oscillator Frequency (ω): 1.0 × 10¹⁵ rad/s

Particle Mass (m): 1 × m_e (electron mass)

Explanation

Particle in a Box: This shows the wave function (ψ) and probability density (|ψ|²) for a quantum particle confined to a one-dimensional box. The walls of the box are infinite potential barriers, forcing the wave function to be zero at the boundaries.

Key observations:

• Wave functions are standing waves with nodes at the boundaries
• Higher energy levels have more nodes
• The probability density shows where the particle is likely to be found

Wave Function Superposition: This shows the combination of two quantum states and how they interfere with each other. The left graph shows the real part of the wave function, while the right shows the probability density.

Key observations:

• Changing the phase difference alters the interference pattern
• Time evolution shows how the superposition changes over time
• The probability density shows regions of constructive and destructive interference

Quantum Harmonic Oscillator: This shows the wave functions and probability densities for a quantum particle in a parabolic potential well. Unlike the particle in a box, the potential extends infinitely but allows for non-zero wave functions at all positions.

Key observations:

• The ground state (n=0) has a Gaussian wave function
• Higher energy states have more nodes
• The wave functions extend into classically forbidden regions (quantum tunneling)