(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi, this is basically a particle in a box problem but V(x) is sinusoidal inside the box.

V(x)=-Asin(pi x/a) 0<x<a

V(x)=Infinity otherwise

A: depth of the well

In the question, it asks me to plot the first 4 eigenfunctions.

3. The attempt at a solution

After plugging the sinusoidal potential function into the Schrodinger equation, the equation looks like:

y''(x)-(E+Asin(Cx)y(x)=0

I don't have a clue about solving this. I've been looking at the quantum mechanics books and diff. eqs. books for hours but I can't seem to find anything useful. I'm using Mathematica I cannot solve it numerically since I don't know "E".

Is there any place that I can look at for a possible solution or direction? Thank you.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Infinite potential well with V(x)=Asin(x pi/a)

Can you offer guidance or do you also need help?

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