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Canonical transformations

  1. Dec 6, 2009 #1
    1. The problem statement, all variables and given/known data

    Question 3b from the following file:
    http://phstudy.technion.ac.il/~wn114101/hw/wn2010_hw07.pdf [Broken]

    I know I need to find a generating function for this spacific transformation. but I don't know how to find it, I mean , how I find a spacific transformation for a spacific hamiltonain?
    thnaks
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Dec 6, 2009 #2

    gabbagabbahey

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    Do you know what the Hamiltonian of a one dimensional harmonic oscillator looks like?
     
  4. Dec 7, 2009 #3
    It's the classic expression (H=p^2/2m+kx^2/2)
     
  5. Dec 10, 2009 #4

    gabbagabbahey

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    Right, so (using [itex]P[/itex] and [itex]Q[/itex] instead of 'p' and 'x'), you are looking for a canonical transformation [itex]Q=Q(q,p)[/itex] and [itex]P=P(q,p)[/itex], for which [tex]\frac{1}{2}\left(\frac{1}{q^2}+p^2q^4\right)\to \frac{P^2}{2m}+\frac{kQ^2}{2}[/itex] (give or take a constant)...what does the fact that the transformation is canonical tell you?
     
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