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

Journal Article · Sat Apr 15 00:00:00 EDT 2006 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2005.11.005· OSTI ID:20767000

Chruscinski, Dariusz ^[1]

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1. Institute of Physics, Nicolaus Copernicus University, ul. Grudziadzka 5/7, 87-100 Torun (Poland)

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.

• OSTI ID: 20767000
• Journal Information: Annals of Physics (New York), Vol. 321, 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); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENVALUES
HAMILTONIANS
HARMONIC OSCILLATORS
POTENTIALS
QUANTIZATION
QUANTUM MECHANICS
TWO-DIMENSIONAL CALCULATIONS