1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question about canonical transformation

  1. Dec 4, 2013 #1
    I was going through my professor's notes about Canonical transformations. He states that a canonical transformation from (q, p) to (Q, P) is one that if which the original coordinates obey Hamilton's canonical equations than so do the transformed coordinates, albeit for a different Hamiltonian. He then considers, as an example the Hamiltonian


    with a transformation

    [tex]Q = q,[/tex]
    [tex]P = \sqrt{p} - \sqrt{q}.[/tex]

    The notes state that "this transformation is locally canonoid with respect to H," and that in the transformed coordinates the new Hamiltonian is

    [tex] K = \frac{1}{3} \left( P + \sqrt{Q} \right)^3.[/tex]

    I don't understand how we know that this is locally canonical, or what it really even means to be locally canonical. Also, where do we get K from. Since the inverse transformation would be

    [tex]p=\left( P + \sqrt{Q} \right)^2[/tex]

    why isn't the new Hamiltonian

    [tex]K= \frac{1}{2} \left(P + \sqrt{Q} \right)^4,[/tex]

    where all I've done is plug the inverted transformation into the original Hamiltonian. I'm a bit confused by all this. Would appreciate any help.

  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Question about canonical transformation