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Tomograms in the Quantum-Classical transition

V. I. Man'ko·G. Marmo·A. Simoni·A. Stern·F. Ventriglia
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Abstract

The quantum-classical limits for quantum tomograms are studied and compared with the corresponding classical tomograms, using two different definitions for the limit. One is the Planck limit where $\hbar \to 0$ in all $\hbar $-dependent physical observables, and the other is the Ehrenfest limit where $\hbar \to 0$ while keeping constant the mean value of the energy.The Ehrenfest limit of eigenstate tomograms for a particle in a box and a harmonic oscillatoris shown to agree with the corresponding classical tomograms of phase-space distributions, after a time averaging. The Planck limit of superposition state tomograms of the harmonic oscillator demostrating the decreasing contribution of interferences terms as $\hbar \to 0$.

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V. I. Man'ko, G. Marmo, A. Simoni, A. Stern, F. Ventriglia. 2005-05-30. Tomograms in the Quantum-Classical transition. https://doi.org/10.1016/j.physleta.2005.05.090

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