# Time-Dependent Superposition of Particle-in-a-Box Eigenstates

Time-Dependent Superposition of Particle-in-a-Box Eigenstates

This Demonstration looks at a time-dependent superposition of quantum particle-in-a-box eigenstates, , where the eigenstates and eigenenergies are given by (x)=sin and =, respectively. The Hamiltonian for this system is =, and its expectation value gives the energy . The upper panel shows the complex wavefunction , where the shape is its modulus and the coloring is according to its argument (the range to corresponds to colors from red to magenta). The lower panel shows the eigenenergies in blue and the energy of the superposition state in red.

ψ(x,t)=(x)

6

∑

n=1

c

n

-t/ℏ

E

n

e

ϕ

n

ϕ

n

2

L

nπx

L

E

n

2

n

2

π

2

ℏ

2m

2

L

H

2

p

2m

=

H

ψ(x,t)ψ(x,t)

H

〈ψ(x,t)ψ(x,t)〉

ψ(x,t)

0

2π