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Title: Flat minimal quantizations of Stäckel systems and quantum separability

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. - Highlights: • Using Stäckel transform, separable Hamiltonians are expressed by flat coordinates. • The concept of admissible flat minimal quantizations is developed. • The class of Stäckel systems, separable after minimal flat quantization is established. • Separability of related stationary Schrödinger equations is presented in explicit form.

Authors:
 [1];  [1];  [2]
  1. Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań (Poland)
  2. Department of Mathematics, Ýzmir University of Economics, 35330, Balçova, Ýzmir (Turkey)
Publication Date:
OSTI Identifier:
22403466
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 351; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COORDINATES; EUCLIDEAN SPACE; HAMILTONIANS; HERMITIAN OPERATORS; HILBERT SPACE; QUANTIZATION; SCHROEDINGER EQUATION

Citation Formats

Błaszak, Maciej, Domański, Ziemowit, and Silindir, Burcu. Flat minimal quantizations of Stäckel systems and quantum separability. United States: N. p., 2014. Web. doi:10.1016/J.AOP.2014.08.015.
Błaszak, Maciej, Domański, Ziemowit, & Silindir, Burcu. Flat minimal quantizations of Stäckel systems and quantum separability. United States. https://doi.org/10.1016/J.AOP.2014.08.015
Błaszak, Maciej, Domański, Ziemowit, and Silindir, Burcu. 2014. "Flat minimal quantizations of Stäckel systems and quantum separability". United States. https://doi.org/10.1016/J.AOP.2014.08.015.
@article{osti_22403466,
title = {Flat minimal quantizations of Stäckel systems and quantum separability},
author = {Błaszak, Maciej and Domański, Ziemowit and Silindir, Burcu},
abstractNote = {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. - Highlights: • Using Stäckel transform, separable Hamiltonians are expressed by flat coordinates. • The concept of admissible flat minimal quantizations is developed. • The class of Stäckel systems, separable after minimal flat quantization is established. • Separability of related stationary Schrödinger equations is presented in explicit form.},
doi = {10.1016/J.AOP.2014.08.015},
url = {https://www.osti.gov/biblio/22403466}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = ,
volume = 351,
place = {United States},
year = {Mon Dec 15 00:00:00 EST 2014},
month = {Mon Dec 15 00:00:00 EST 2014}
}