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A. Mohamed Meziane

Publications and source records attributed to A. Mohamed Meziane.

2 recordsLinked to original sources
arXiv2007

Band theory in the context of the Hamilton-Jacobi formulation

In the one-dimensional periodic potential case, we formulate the condition of Bloch periodicity for the reduced action by using the relation between the wave function and the reduced action established in the context of the equivalence postulate of quantum mechanics. Then, without appealing to the wave function properties, we reproduce the well-known dispersion relations which predict the band structure for the energy spectrum in the Krönig-Penney model.

quant-ph↗
arXiv2007

The Three-Dimensional Quantum Hamilton-Jacobi Equation and Microstates

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.

quant-ph↗