# Representing Wavefunction as Superposition of Eigenstates

## Homework Statement

A particle in the infinite square well with V(x)=0 for 0<x<a and V(x)=infinity otherwise has the initial (t=0) wave function:

psi(x,0)=Ax for 0<x<a/2
psi(x,0)= A(a-x) for a/2<x<a

1) Sketch psi and psi^2 (DONE)
2) Determine A [DONE - 2*sqrt(3)*a^(-3/2)]
3) Find psi(x,t) (HELP!)
4) What is the probability that a measurement of the energy yields the first eigenenergy level E1 of this infinite square well?
5) Find the expectation value of the energy.

## Homework Equations

Psi(x,t)=SUMMATION[Cn*Psi n] = SUM[Cn sin((n*pi*x)/a)

Cn=int(psi(x,0)sin((n*pi*x)/a)
Cn=int(A*x*sin((n*pi*x)/a)) + int(A(a-x)*sin((n*pi*x)/a))

Questions!

Do I replace the 'n's in sin((n*pi*x)/a) with 1 and 2 when I'm solving for Cn? Am I trying to represent the wavefunction as a sum of sin((pi*x)/a) and sin((2*pi*x)/a) .... or do I just leave the quantum number n in my equations?

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cepheid
Staff Emeritus
Don't forget that the summation you have expressed is actually for $\Psi(x,0)$ and that the time dependence comes in as an extra exponential factor multiplying each eigenfunction.