What are the energy and momentum eigenfunctions for specific quantum systems?

[UrbanXrisis]

just a general and quick question because I'm making a formula sheet for my test tomorrow:

What is the energy eigenfunction for a free particle and what is the momentum eigenfunction for a particle in a box?

 

[quasar987]

Why are you asking?!? If you're taking a QM class, surely you've covered these things in class and they are in your textbook!

 

[UrbanXrisis]

i skipped QM and went into quantum theory so i never went over this. this isn't talked about in my book. all i need to know is the energy eigenfuction for a free particle please? Oh and momentum eigenvalues for a particle in a box?

 

[quasar987]

http://en.wikipedia.org/wiki/Free_particle

http://en.wikipedia.org/wiki/Particle_in_a_box#Solution

 

[UrbanXrisis]

so I've went there already, and coundt find them, which is why I'm asking on this forum. maybe i just can't spot them out?

 

[christianjb]

That's an interesting Q though.

What are the momentum eigenfunctions of a particle in a box? The FT of the waves between the walls must look a bit weird.