Preset
Free Particle
k₀ = 25, σ₀ = 0.14
Narrow Packet
rapid spread — high Δk
Wide Packet
slow spread — low Δk
High Momentum
k₀ = 45, fast v₀
Low Momentum
k₀ = 10, slow v₀
Wavenumber k₀
25
Initial width σ₀
0.140
Speed
1.0×
ℑ Im(ψ)
~ Envelope
vₚ marker
⏸ Pause
↺ Reset
Gaussian packet spreads as
Δx(t) = σ₀ √(1 + t²/4σ₀⁴).
Group velocity v₉ = k₀, phase
velocity vₓ = k₀/2 (blue dot).
k₀ =
25
v₉ =
25
vₓ =
12.5
σ(t) =
0.140
Δx·Δk =
0.500
t =
0.000
iℏ∂ψ/∂t = −(ℏ²/2m)∂²ψ/∂x²
k₀
— wavenumber (momentum / ℏ)
σ₀
— initial spatial width
vₓ marker
— phase crest (half v₉)
Space
— pause / play