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Title: Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D parabolic potential barrier

Abstract

We show that quantum Bateman's system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba.

Authors:
 [1]
  1. Institute of Physics, Nicolaus Copernicus University, ul. Grudziadzka 5/7, 87-100 Torun (Poland)
Publication Date:
OSTI Identifier:
20767000
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 321; Journal Issue: 4; Other Information: DOI: 10.1016/j.aop.2005.11.005; PII: S0003-4916(05)00244-7; Copyright (c) 2005 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; EIGENVALUES; HAMILTONIANS; HARMONIC OSCILLATORS; POTENTIALS; QUANTIZATION; QUANTUM MECHANICS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Chruscinski, Dariusz. Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D parabolic potential barrier. United States: N. p., 2006. Web. doi:10.1016/j.aop.2005.11.005.
Chruscinski, Dariusz. Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D parabolic potential barrier. United States. https://doi.org/10.1016/j.aop.2005.11.005
Chruscinski, Dariusz. 2006. "Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D parabolic potential barrier". United States. https://doi.org/10.1016/j.aop.2005.11.005.
@article{osti_20767000,
title = {Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D parabolic potential barrier},
author = {Chruscinski, Dariusz},
abstractNote = {We show that quantum Bateman's system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba.},
doi = {10.1016/j.aop.2005.11.005},
url = {https://www.osti.gov/biblio/20767000}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = 4,
volume = 321,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2006},
month = {Sat Apr 15 00:00:00 EDT 2006}
}