A particle in an infinite square well

[Quatumphysicshelp]

Homework Statement

The homework is in a photo, a long with some to most of my work.

Relevant Equations

There are a lot of equations....

What I am lost about is b, rather the rest of B. I am not sure what it means by probability density and a stationary state.

 

[Linguisturn]

By probability density, it most likely means the probability density function. When a quantum state is stationary (and remember that it's the hamiltonian's eigenvector), that just means it does not grow throughout the course of time. That's how i'd put it.

 

[kuruman]

You have written down $\psi(x,t)$. The problem is asking you to find "the probability density $|\psi(x,t)|^2.$ How do you interpret that?
Your textbook must have a definition for stationary state. If you cannot find it, look it up on the web.