- #1

fanieh

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In the 1930s, John von Neumann consolidated ideas from Bohr, Heisenberg and Schrodinger and placed the new quantum theory in Hilbert space.

In Hilbert space, a vector represents the Schrodinger wave function.

I know they are equivalent..

Furthermore… When describing more than one particle in the Schrodinger wave function.. the wave no longer occur in 3D space, but in higher dimensional mathematical space.

Now the Hamiltonian, I’m aware that The Hamiltonian is the sum of the kinetic energies of all the particles, plus the potential energy of the particles associated with the system. For different situations or number of particles, the Hamiltonian is different since it includes the sum of kinetic energies of the particles, and the potential energy function corresponding to the situation.

Now let’s go to classical Hamilton-Jacobi equation. This is used by Bohmian Mechanics to

represent the wave function. But first let’s go to classical Hamilton-Jacobi formalism.

__http://www.jh-inst.cas.cz/~kapralova/QUANTCLASS/goldstein.html__

“Usually, the classical mechanics is understood in terms of trajectories, that is in terms of delta functions in the phase space. However, the Hamilton- Jacobi formalism of classical mechanics allows us to understand even the purely classical mechanics in terms of moving wavefronts in space.”

How do you understand the classical Hamilton- Jacobi formalism. Is it trying to model all the wave function in higher dimensional mathematical space as waves in 3D space?? How does it differ to the pure Hamiltonian formalism?