# Wave Function as superposition of eigenstates

1. Apr 19, 2007

### mavyn

Hi!

How can I write the wave function of a particle in an infinite box (in the state n) as a superposition of the eigenstates of the momentum operator?

the wave function is:

PHIn(x,t) = sqrt(2/a) * Sin(n * PI/a * x) * exp(-i En/h * t)

Thanks for your help!

2. Apr 20, 2007

### gammamcc

well what are the basic solutions to py =ky for the momentum operator P? (BTW what are the solution of y"=ky?)

Can you express, say, the Sine function in term of these functions? (Try the expressing Sine in terms of exponentials via Euler's Identity.)