Two quantization approaches to the Bateman oscillator model

We consider two quantization approaches to the Bateman oscillator model. One is Feshbach-Tikochinsky's quantization approach reformulated concisely without invoking the \({\mathit{SU}(1,1)}\) Lie algebra, and the other is the imaginary-scaling quantization approach developed originally for the...

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Bibliographic Details
Published in:arXiv.org 2019-02
Main Authors: Deguchi, Shinichi, Fujiwara, Yuki, Nakano, Kunihiko
Format: Article
Language:English
Subjects:
Eigenvectors
Energy spectra
Lie groups
Measurement
Norms
Oscillators
Quantum theory
Scaling
Online Access:Get full text
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Summary:We consider two quantization approaches to the Bateman oscillator model. One is Feshbach-Tikochinsky's quantization approach reformulated concisely without invoking the \({\mathit{SU}(1,1)}\) Lie algebra, and the other is the imaginary-scaling quantization approach developed originally for the Pais-Uhlenbeck oscillator model. The latter approach overcomes the problem of unbounded-below energy spectrum that is encountered in the former approach. In both the approaches, the positive-definiteness of the squared-norms of the Hamiltonian eigenvectors is ensured. Unlike Feshbach-Tikochinsky's quantization approach, the imaginary-scaling quantization approach allows to have stable states in addition to decaying and growing states.
ISSN:2331-8422
DOI:10.48550/arxiv.1807.04403