Particle in a Box
Time-dependent Schrodinger equation in 1D — wavefunction evolution, eigenstates, quantum revivals
Wavefunction
Initial state
Gaussian wave packet
Eigenstate n=1
Eigenstate n=2
Eigenstate n=3
Superposition n=1+2
Superposition n=1+2+3
Coherent state (n=1..5)
Packet center x0:
0.30
Packet width sigma:
0.08
Initial momentum k0:
20
Time speed:
1.0
Reset
Pause
Energy levels En = n^2 * pi^2 / 2
TDSE:
psi(x,t) = sum cn * phi_n(x) * exp(-i*En*t)
phi_n(x) = sqrt(2) sin(n*pi*x), En = n^2*pi^2/2 (hbar=m=L=1)
Green:
Re(psi)
Orange:
Im(psi)
Blue fill:
|psi|^2
Watch for
quantum revivals
— at t=T_rev the packet reconstructs itself. Superposition states show quantum beating.