Flat minimal quantizations of Stäckel systems and quantum separability

Journal Article · Mon Dec 15 00:00:00 EST 2014 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2014.08.015· OSTI ID:22403466

Błaszak, Maciej ^[1]; Domański, Ziemowit ^[1]; Silindir, Burcu ^[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)

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.

• OSTI ID: 22403466
• Journal Information: Annals of Physics (New York), Vol. 351; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COORDINATES
EUCLIDEAN SPACE
HAMILTONIANS
HERMITIAN OPERATORS
HILBERT SPACE
QUANTIZATION
SCHROEDINGER EQUATION