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A Most General form of Canonical Transformation

  1. Apr 12, 2016 #1
    How do I go about finding the most general form of the canonical transformation of the form
    Q = f(q) + g(p)
    P = c[f(q) + h(p)]
    where f,g and h are differential functions and c is a constant not equal to zero. Where (Q,P) and (q,p) represent the generalised cordinates and conjugate momentum in the new and old system
  2. jcsd
  3. Apr 12, 2016 #2


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    2016 Award

    Isn't this "homework" of some kind? You should post it in the Homework and Coursework section! Anyway, here's some hint:

    I'd try to determine constraints on the functions by evaluating the Poisson brackets which must be
    $$\{Q,Q\}=\{P,P \}=0, \quad \{Q,P \}=1$$
    in order to have a canonical transformation.
  4. Apr 12, 2016 #3
    I am done all that with certain kinds of relationship between (Q,P) and (q,p) but I am unable to do so with this general formula that does not give the function itself
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