Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/2493
Title: Exactly solvable quantum Sturm-Liouville problems
Authors: Atılgan Büyükaşık, Şirin
Pashaev, Oktay
Tığrak Ulaş, Esra
Keywords: Quantum mechanics
Sturm–Liouville problem
Oscillators
Lagrangian mechanics
Polynomials
Issue Date: 2009
Publisher: American Institute of Physics
Source: Atılgan Büyükaşık, Ş. , Pashaev, O., and Tığrak Ulaş, E. (2009). Exactly solvable quantum Sturm-Liouville problems. Journal of Mathematical Physics, 50(7). doi:10.1063/1.3155370
Abstract: The harmonic oscillator with time-dependent parameters covers a broad spectrum of physical problems from quantum transport, quantum optics, and quantum information to cosmology. Several methods have been developed to quantize this fundamental system, such as the path integral method, the Lewis-Riesenfeld time invariant method, the evolution operator or dynamical symmetry method, etc. In all these methods, solution of the quantum problem is given in terms of the classical one. However, only few exactly solvable problems of the last one, such as the damped oscillator or the Caldirola-Kanai model, have been treated. The goal of the present paper is to introduce a wide class of exactly solvable quantum models in terms of the Sturm-Liouville problem for classical orthogonal polynomials. This allows us to solve exactly the corresponding quantum parametric oscillators with specific damping and frequency dependence, which can be considered as quantum Sturm-Liouville problems.
URI: http://dx.doi.org/10.1063/1.3155370
http://hdl.handle.net/11147/2493
ISSN: 0022-2488
0022-2488
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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