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Hamiltonian as Legendre transformation?

  1. Jun 4, 2010 #1
    The definition of a Legendre transformation given on the Wikipedia page http://en.wikipedia.org/wiki/Legendre_transformation is: given a function f(x), the Legendre transform f*(p) is


    Two questions: what does [tex]\max_x[/tex] mean here? And why is it not (explicitly?) included in the definition of the Hamiltonian


    if the Hamiltonian is a Legendre transformation?
  2. jcsd
  3. Jun 4, 2010 #2
    I get it. If we want to maximize


    then we set [tex]g'(x)=0[/tex] which is the same as putting [tex]p=f'(x)[/tex]. In mechanics this amounts to

    [tex]p=\frac{\partial L}{\partial\dot{q}}[/tex]

    Well.. thanks to anyone who read and at least thought about replying. :-)
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