Time Evolution of the Wavefunction in a 1D Infinite Square Well

​
a
1
1
p
1
0
a
2
0
p
2
0
a
3
0
p
3
0
t
0
Ψ(x, t = 0) = ∑
ψ
n
c
n
(x)
Ψ(x, t) = ∑
c
n
ψ
n
(x)
i
E
n
t/h
e
c
1
= 1
c
2
= ​0
c
3
= 0
<H> = 1
This Demonstration shows some solutions to the time-dependent Schrödinger equation for a 1D infinite square well. You can see how wavefunctions and probability densities evolve in time. You can set initial conditions as a linear combination of the first three energy eigenstates.

Details

Vary the time
t
to see the evolution of the wavefunction of a particle of mass
m
in an infinite square well of length
L
. Initial conditions are a linear combination of the first three energy eigenstates
ψ
n
. The amplitude of each coefficient is set by the
a
sliders. The phase of each coefficient at
t=0
is set by the
p
sliders. The wavefunction is automatically normalized.
Position is in units of
L
.
Ψ
is in units of
-1/2
L
.
ρ
is in units of
-1
L
.
Energy is in units of
2
ℏ
2
π
/2
2
mL
.
Time is in units of
ℏ/(2π
energy units).

External Links

Schrödinger Equation (ScienceWorld)
Infinite Square Potential Well (ScienceWorld)
Time-Dependent Superposition of Particle-in-a-Box Eigenstates

Permanent Citation

Jonathan Weinstein, (University of Nevada, Reno)
​
​"Time Evolution of the Wavefunction in a 1D Infinite Square Well"​
​http://demonstrations.wolfram.com/TimeEvolutionOfTheWavefunctionInA1DInfiniteSquareWell/​
​Wolfram Demonstrations Project​
​Published: June 13, 2011