Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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]

    where

    [tex]u=\frac{dr}{dt}[/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:

    http://en.wikipedia.org/wiki/Hamilton–Jacobi_equation

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


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

    best regards,

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

    Any ideas left?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Hamilton-Jacobi-Equation (HJE)
Loading...