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Energy spectrum of charged particle

  1. Jan 7, 2013 #1
    1. The problem statement, all variables and given/known data

    M4QnP.png

    2. Relevant equations

    a(+) = (-ip+mwx)/(2hmw)^1/2
    a() = (+ip+mwx)/(2hmw)^1/2

    3. The attempt at a solution

    can i use these operators to solve this problem? please help me i need to give this homework tomorrow morning :confused:
     
  2. jcsd
  3. Jan 7, 2013 #2

    Simon Bridge

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    I imagine the method you should use will depend on the context of your lessons so far.
    eg. I'd want to use perturbation theory. If you've just done some of that in class, then there's your approach.
     
  4. Jan 7, 2013 #3
    thank you but we did not do perturbation theory. actually this is takehome and it can be further subject which we did not know. if it is about perturbation theory how can i start and how can i solve it? what is the way of it? i have 3-4 hour :)
     
  5. Jan 7, 2013 #4

    Dick

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    How about completing the square in x in the Hamiltonian?
     
  6. Jan 7, 2013 #5
    This problem can be solved exactly. Just complete the square first for x and solve the resulting harmonic oscillator problem using the transformation between {x,p} and {a, a'}.
     
  7. Jan 7, 2013 #6

    Simon Bridge

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    What they said - if it were perturbation theory, it would say (somewhere) that the uniform field is "weak".
     
  8. Jan 7, 2013 #7

    Dick

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    This is actually a good problem for comparing the results of perturbation theory with an exact solution. I think I've seen it used that way.
     
  9. Jan 7, 2013 #8
    thank you for your help. i will try now.
     
  10. Jan 7, 2013 #9

    Simon Bridge

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    I know I've seen it this way. It's almost routine in some courses ... hence my knee-jerk reaction to check that was not the case this time.

    Of course this means we could probably look up the solution...
     
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