- #1

- 14

- 2

## Homework Statement

"A particle of mass m is in the ground state of a one-dimensional infinite square well with walls at x=0 and x=a.

[tex]\psi_1(x) =\sqrt{\frac{2}{a}}sin(\frac{\pi x}{a})[/tex],

E

_{1}=[tex]\frac{h^2\pi ^2}{2ma^2}[/tex]*

What is the initial wave function [tex]\Psi(x,0)?[/tex]

*[tex]h[/tex] is supposed to be h bar, I just couldn't find it)

## Homework Equations

## The Attempt at a Solution

My attempt: If the general solution is a superposition of all stationary states, [tex]\Psi(x,t)=\sum c_n\psi_ne^\frac{-iE_nt}{h}[/tex], at t=0, [tex]\Psi(x,0)=\sum c_n\psi_n[/tex]. Also, at this time, the particle is in the ground state (n=1), so: [tex]\Psi(x,0)=c_1\psi_1[/tex]. Do I assume c

_{1}=1 at this point, because the wave function "collapses" once the energy becomes known? I'm just not sure if I understand exactly what happens when the known data is given.

The solution itself is supposed to be [tex]\Psi(x,0)=\psi_1(x) =\sqrt{\frac{2}{a}}sin(\frac{\pi x}{a})[/tex].