Infinite Square Well — Superposition & Quantum Sloshing
ψ = c₁ψ₁e
−iE₁t/ħ
+ c₂ψ₂e
−iE₂t/ħ
: the probability density oscillates at frequency ΔE/h = 307 THz for a 1 nm well.
c₁ (amplitude weight)
0.71
Speed
1×
⏸ Pause
|ψ(x,t)|² — probability density
t =
0.00
fs | ⟨x⟩ =
0.500
L
⟨E⟩ =
0.940
eV | T_period =
3.67
fs
L = 1 nm | E₁ = 0.376 eV | E₂ = 1.504 eV | ΔE = 1.128 eV
⟨x⟩(t) = L/2 − 2c₁c₂·(16L/9π²)·cos(ΔEt/ħ)
Pure ψ₁: ⟨x⟩ = L/2 fixed (no sloshing)
⟨x⟩(t) — position expectation (last 2 periods)
Oscillation amplitude:
0.181
L | c₂ =
0.71