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Canonical Transformation

  1. Feb 23, 2009 #1
    1. The problem statement, all variables and given/known data

    Verify that

    q_bar=ln(q^-1*sin(p))

    p_bar=q*cot(p)


    * represents muliplication

    sorry i don't know how to use the programming to make it look better



    2. The attempt at a solution

    my problem is that i really have no clue what is going on. I have read the section, reread the section, then looked on online just to try and find an example. I am much more of a visual learner so reading doesn't help all the time.

    I guess i'm looking for some guidance of what/how to do. and not even this proble, but just an example or process.
     
  2. jcsd
  3. Feb 23, 2009 #2

    malawi_glenn

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    Science Advisor
    Homework Helper

    a canonical transformation preserves the poission bracket

    i.e the possion bracket of p and q: {q,p}_(p,q) = 1

    thus if {q_bar, p_bar}_(p,q) = 1, then it is a canonical transformation.

    (there are more ways to show it, like if there exists a generation function.. but I like the poission bracket the most, it is easy to remember)

    The poission bracket is defined as
    [tex]\left\lbrace f,g \right\rbrace _{(q,p)} = \dfrac{\partial f}{\partial q}\dfrac{\partial g}{\partial p} -\dfrac{\partial f}{\partial p}\dfrac{\partial g}{\partial q} [/tex]
     
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