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Quantum particle in a 2 dimensional box

by Unskilled
Tags: dimensional, particle, quantum
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Unskilled
#1
Jun5-07, 10:52 AM
P: 13
1. The problem statement, all variables and given/known data
I need some help

http://www.fysik.uu.se/kurser/1tt306...rt-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.
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malawi_glenn
#2
Jun5-07, 11:43 AM
Sci Advisor
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P: 4,738
Quote Quote by Unskilled View Post
1. The problem statement, all variables and given/known data
I need some help

http://www.fysik.uu.se/kurser/1tt306...rt-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
#3
Jun6-07, 11:27 AM
HW Helper
P: 2,567
Note there's no qualititative difference between the x and y directions. You could write the wavefunction more symmetrically as:

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

They just used some trig identities to rewrite this.


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