Hamilton-Jacobi equation and particle-wave motion

  • #1
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Main Question or Discussion Point

I've seen somwhere a claim that Hamilton-Jacobi euqation is the only formulation of classical mechanics which can treat motion of particle as wave motion. There was something about hamilton prinicpal function, hamilton characteristic function and one of these change in time like wavefront or something like this :P Sorry for not beeing clear, I don't understand the math behind but the claim sounds really intresting. Mainly beacuse QM does the same - there is a wave associate with particle.

Does anyone have good source of knowledge for this topic or can explain this?
 

Answers and Replies

  • #2
963
213
there is a wave associate with particle.
in the classical limit the schrodinger equation goes to H - J equation ...

we see that in the classical limit h→ 0 the Schrodinger equation is just the Hamilton-Jacobi equation.

The H-J equation was a partial differential equation that could be solved with any choice of function at t = 0.

This function acts like the wavefunction that we encounter in quantum mechanics.

For the H-J equation we will take a real solution S, and thus we will indeed be dropping......
pl. see the discussion in ref. below p-8

<http://www.physics.ohio-state.edu/~mathur/821hj.pdf>
 

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