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Quantum - Projection Probability - Projection amplitudes for SHO states.

  1. Nov 16, 2009 #1
    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!


    Thanks for any hints or help you can give me!

    Andrew
     

    Attached Files:

    Last edited: Nov 16, 2009
  2. jcsd
  3. Nov 16, 2009 #2
    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
     

    Attached Files:

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