Quantum damped oscillator I: Dissipation and resonances

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

DOI:https://doi.org/10.1016/j.aop.2005.11.004· OSTI ID:20767001

Chruscinski, Dariusz ^[1]; Jurkowski, Jacek ^[1]

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

Quantization of a damped harmonic oscillator leads to so called Bateman's dual system. The corresponding Bateman's Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states which are responsible for the irreversible quantum dynamics of a damped harmonic oscillator.

• OSTI ID: 20767001
• Journal Information: Annals of Physics (New York), Vol. 321, Issue 4; Other Information: DOI: 10.1016/j.aop.2005.11.004; PII: S0003-4916(05)00243-5; 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
EIGENVECTORS
HAMILTONIANS
HARMONIC OSCILLATORS
QUANTIZATION
QUANTUM MECHANICS
RESONANCE