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Can I substitute the new coordinates in the old hamiltonian?

  1. Mar 27, 2015 #1
    We went over this concept quite fast in class and there is one thing that confused me:

    When transforming from a set of ##q_i## and ##p_i##to ##Q_i## and ##P_i##, if one checks that the transormations are canonical the new Hamiltonian ##K(Q_i, P_i)## obeys exactly the same equations.This has been proven.

    Question: How does one in general find this new Hamiltonian ##K(Q_i, P_i)##? I have gotten the impression that it's not as easy as just substituting the transformations into the old coordinates, or is it?
     
  2. jcsd
  3. Mar 28, 2015 #2

    Orodruin

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    The Hamiltonian is a function on phase space. It does not matter what coordinates you use to express it.
     
  4. Mar 28, 2015 #3
    This means that I can just substitute my old coordinates in function of the new coordinates into my old hamiltonian to get the new hamiltonian?
     
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