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Hamilton-Jacobi-Equation (HJE)

  1. Sep 27, 2009 #1
    Hi all!

    I was studying the HJ-formalism of classical mechanics when I came upon a modified HJE:

    [tex](\nabla S)^2=\frac{1}{u^2}(\frac{\partial S}{\partial t})^2[/tex]



    and [tex]dr=(dx,dy,dz)[/tex] is the position vector.
    (I read the derivation and it's ok)

    Now, u is interpreted to be the wave velocity of the so called 'action waves' in phase space.

    However, my book (Nolting, Volume 2) states that this is a wave equation, or at least a special nonlinear case of the popular wave equation

    [tex]\nabla^2S=\frac{1}{u^2}\frac{\partial^2}{\partial t^2}S[/tex]

    which is somehow unclear to me, as the squares in both equations mean different things.

    A similar statement is also made in Wikipedia:


    (cf. Eiconal apprpximation and relationship to the Schrödinger equation)

    I hope someone of you can explain this to me :)

    best regards,

  2. jcsd
  3. Sep 28, 2009 #2
    Hmmm, haven't fould anything so far..

    Any ideas left?
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