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Canonical Transformations

  1. Apr 5, 2015 #1
    1. The problem statement, all variables and given/known data
    Show that x = 2qa/sin(T) and p = 2qa.cos(T) is a canonical transformation
    into new coordinates T and momentum q.

    2. Relevant equations


    3. The attempt at a solution
    It looks easy, I've tried matrix/jacobi method, and symplectic method. But these two seem to be not canonical. Am I missing something? The question doesn't give anything else. Do I have to find a generating function to prove that they are canonical? But then it'd would be silly, because the professor is very clear about these things. If he wanted to see a F generating function he would have said so.
     
  2. jcsd
  3. Apr 6, 2015 #2

    MarcusAgrippa

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    Gold Member

    Clue: do you have any theorems that provide necessary and sufficient conditions for a transformation to be canonical?
     
  4. Apr 7, 2015 #3
    I re-correct myself, the prof. is an *******. He hadn't mentioned that we had to use a generating function. now I got it. thanks anyway.
     
  5. Apr 7, 2015 #4

    MarcusAgrippa

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    Gold Member

    That's not nice. I'm sure your prof is a very nice fellow.

    Incidentally, there are several different methods that you might have used to show that the given transformation is canonical.
     
  6. Apr 7, 2015 #5
    Yeah not telling which method we "must" use is not nice either.
    Anyway after trying to do 3 hws each week, and spending a huge chunk of time,
    people can get mad. Also no need to be politically correct here.
     
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