Wave Packet Evolution Visualizer

Quantum Wave Packet Evolution

Initial Width (σ) 1.0

Momentum (k₀) 2.0

Particle Mass (m) 1.0

Time Evolution

Physical Explanation

This simulation shows the time evolution of a Gaussian wave packet in quantum mechanics. The wave packet represents the probability amplitude of finding a quantum particle at position x.

The initial wave function is given by:

ψ(x,0) = (2πσ²)^(-1/4) exp[-(x-x₀)²/(4σ²) + ik₀x]

As time progresses, the wave packet spreads due to dispersion. The time evolution is governed by the Schrödinger equation:

iħ∂ψ/∂t = -ħ²/(2m) ∂²ψ/∂x²

Key observations:

• Narrower initial packets (small σ) spread faster
• The group velocity is v = ħk₀/m
• The phase velocity is v_phase = ω/k = ħk/(2m)
• The uncertainty principle ΔxΔp ≥ ħ/2 is clearly visible