Solve Infinite Square Well: Homework Statement

[jaydnul]

Homework Statement

The wording of the question is throwing me off. It is a standard inf. pot. well problem and we are given the initial position of the particle to be in the left fourth of the box,

$\Psi(x,0)=\sqrt{\frac{4}{a}}$

We are asked to a) write the expansion of the wave function in terms of energy eigenfunctions, b) explicitly compute the expansion coefficients, and c) give an expression for psi at later times.

Homework Equations

$E_n=\frac{n^2\pi^2\hbar^2}{2ma^2}$

The Attempt at a Solution

[/B]
I got b) and c) (I can show my work if necessary)

b) $c_n=\frac{4\sqrt{2}}{n\pi}$ for n= odd
$c_n=0$ for n= even

c) some long expression that I don't want to latex f I don't have to, but will if needed (on my phone :) )

But for a), I would think E_n would be the same as any inf. pot. well problem, wouldn't it? So
$E_n=\frac{n^2\pi^2\hbar^2}{2ma^2}$. Is this right?

 

[jaydnul]

Like usual, writing it out on PF helped me solve the problem. At t=0, $k_n=\frac{4n\pi}{a}$ which allows the calculation of energy.

Thanks anyways

 

[tacosforlife]

What did you get for part a) ?? I am stuck and I am confused what the first step should be. Thanks.

 

[Simon Bridge]

Welcome to PF;

What did you get for part a) ?? I am stuck and I am confused what the first step should be. Thanks.

You will need to work out what $\psi$ (the initial position wavefunction) is from the description - show us what you got along with your reasoning.

For part (a) start with: $$\psi = \sum_n c_n\psi_n : \hat H\psi_n=E_n\psi_n$$ ... you should have notes for what each $\psi_n$ will be so you can look them up.

 

[paranormal]

I would first clarify any confusion about the wording of the question with the instructor. It is important to have a clear understanding of the task at hand before attempting to solve it.

Assuming that the question is asking for the expansion of the wave function in terms of energy eigenfunctions, then your attempt at a solution seems correct. The energy eigenfunctions for an infinite square well are indeed given by E_n=\frac{n^2\pi^2\hbar^2}{2ma^2}. However, it is always good practice to show your work and explain your reasoning to ensure that your solution is understood and can be replicated by others.

If the question is asking for something else, it would be helpful to provide more context or information about the problem. As a scientist, it is important to clearly communicate and explain your thought process, assumptions, and results.