The Three-Dimensional Quantum Hamilton-Jacobi Equation and Microstates

Details The Three-Dimensional Quantum Hamilton-Jacobi Equation and Microstates The Three-Dimensional Quantum Hamilton-Jacobi Equation and Microstates

2007-01-22

arxiv.org/abs/quant-ph/0701159v1

Int. J. Theo. Phys. 45 (2006) 1323

Physics

Quantum Physics

16 pages, no figures

Scientific paper

In a stationary case and for any potential, we solve the three-dimensional quantum Hamilton-Jacobi equation in terms of the solutions of the corresponding Schrodinger equation. Then, in the case of separated variables, by requiring that the conjugate momentum be invariant under any linear transformation of the solutions of the Schrodinger equation used in the reduced action, we clearly identify the integration constants successively in one, two and three dimensions. In each of these cases, we analytically establish that the quantum Hamilton-Jacobi equation describes microstates not detected by the Schrodinger equation in the real wave function case.

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