Solve Schrödinger Equation: Need Help

[schnuffi]

Homework Statement

Hi, I've just started this new course about quantum mechanics and it begins, among others, with this question:

[PLAIN]http://img710.imageshack.us/img710/2962/unbenanntfwg.jpg

I'm really at a loss how to approach this one. Can anyone please help?

 

[diazona]

Well, what do you know? How familiar are you with the Schrödinger equation, and the concepts of operators, eigenfunctions, and eigenvalues?

 

[schnuffi]

Thanks for trying to help :D
I know the definitions of those terms that you have mentioned; but, I am not familiar with their mathematical components enough to use them to tackle the problem freely.

 

[diazona]

You've got to make an effort here if you want us to help you, schnuffi.

Suppose this were a problem on an exam. How would you start? Go back to your references (textbook, notes, etc.) and look things up, if you have to.