Quantum particle in a 2 dimensional box

[Unskilled]

Homework Statement

I need some help

http://www.fysik.uu.se/kurser/1tt306/filer/TentKF06+short-answers.pdf

On task 4 a) i don't understand why they have two solutions, one for odd n and the other for even n.

 

[malawi_glenn]

Homework Statement

I need some help

http://www.fysik.uu.se/kurser/1tt306/filer/TentKF06+short-answers.pdf

On task 4 a) i don't understand why they have two solutions, one for odd n and the other for even n.

Hi there, I also study @ Uppsala ;) physics..

It has to do with the parity of the wave functions. Look on the symmetries around x=0. Ground state has zero nodes, 1st excited has one etc. Skiss the potetial and search for symmetry points.

 

[StatusX]

Note there's no qualititative difference between the x and y directions. You could write the wavefunction more symmetrically as:

$$\psi_{nm} = C \sin \left( n \pi \frac{x-(-A)}{A-(-A)} \right) \sin \left( m\pi \frac{y-0}{B-0}\right)$$

They just used some trig identities to rewrite this.