Infinite Square Well with uniform probability density for a/4<x<3a/4

[zoso335]

Homework Statement

The potential for an infinite square well is given by V=0 for 0<x<a and infinite elsewhere. Suppose a particle initially(t=0) has uniform probability density in the region a/4<x<3a/4 :
a.) Sketch the probability density
b.) Write an expression for the wavefunction as t=0
c.) Find the normalization constant
d.) What is the probability of finding the particle in the lowest eigenstate of the well?
e.) What is the probability of finding the particle in the second lowest eigenstate of the well?

Homework Equations

The Attempt at a Solution

I have no idea what to do this for this since the wave function is always described as wavelengths in the well, but since its uniform for a/4<x<3a/4 I don't know how to set it up right

 

[gabbagabbahey]

Hi zoso335, welcome to PF!

I have no idea what to do this for this since the wave function is always described as wavelengths in the well, but since its uniform for a/4<x<3a/4 I don't know how to set it up right

What do you mean by "the wavefunction is always described by wavelengths in the well"?

 

[zoso335]

well the probability density is the magnitude square of the wave function. And, the wave function of an infinite well always fits an integer multiple of half wavelengths. So, since the probability density is uniform, the wave function has to be uniform in this region, but I don't know how to find the wave function outside this region but still within the well.

 

[gabbagabbahey]

the wave function of an infinite well always fits an integer multiple of half wavelengths.

No, the eigenfunctions always fit an integer multiple of half-wavelengths...What are these eigenfunctions? Is it possible for the wavefunction of this particle to be in one of these eigenfunctions? Does it have to be?