Flat minimal quantizations of Stäckel systems and quantum separability |
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Authors: | Maciej Błaszak Ziemowit Domański Burcu Silindir |
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Affiliation: | 1. Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland;2. Department of Mathematics, Izmir University of Economics, 35330, Balçova, Izmir, Turkey |
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Abstract: | In this paper, we consider the problem of quantization of classical Stäckel systems and the problem of separability of related quantum Hamiltonians. First, using the concept of Stäckel transform, natural Hamiltonian systems from a given Riemann space are expressed by some flat coordinates of related Euclidean configuration space. Then, the so-called flat minimal quantization procedure is applied in order to construct an appropriate Hermitian operator in the respective Hilbert space. Finally, we distinguish a class of Stäckel systems which remains separable after any of admissible flat minimal quantizations. |
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Keywords: | Stä ckel system Stä ckel transform Minimal quantization Quantum separability |
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