# Quantum - Projection Probability - Projection amplitudes for SHO states.

1. Nov 16, 2009

### metgt4

Quantum - Projection Probability - "Projection amplitudes for SHO states."

Given the two normalized 2D SHO wave functions <x,y|mx[/SUB ],ny> for the second energy level n = nx + ny = 1 in the mx[/SUB ],ny representation:

<x,y|1,0> = (2/pi)1/2xexp[-(x2+y2)/2]
<x,y|0,1> = (2/pi)1/2yexp[-(x2+y2)/2]

and in the alternative n, m representation <x,y|n,m>

<x,y|1,+1> = (1/pi)1/2(x+iy)exp[-(x2+y2)/2]

<x,y|1,-1> = (1/pi)1/2(x-iy)exp[-(x2+y2)/2]

(a) Construct a table of projection amplitudes between these two similar to Table 7-1 (I'll include this table in the attachments) for photon polarization states.

The question continues, but I would like to work the rest out myself. I just don't seem to understand how to change from one base to the other for this question!

Andrew

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Last edited: Nov 16, 2009
2. Nov 16, 2009

### metgt4

Re: Quantum - Projection Probability - "Projection amplitudes for SHO states."

Am I at all on the right track here? I have a relation between the two bases, but this is as far as I've gotten all week! What I've got is attached.

Thanks!
Andrew

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