Two quantization approaches to the Bateman oscillator model

Journal Article · Mon Apr 15 00:00:00 EDT 2019 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2019.02.004· OSTI ID:22852394

Deguchi, Shinichi ^[1]; Fujiwara, Yuki ^[2]; Nakano, Kunihiko ^[3]

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1. Institute of Quantum Science, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan)
2. Department of Quantum Science and Technology, Graduate School of Science and Technology,Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan)
3. Junior and Senior High School, Shibaura Institute of Technology, Koto-ku, Tokyo 135-8139 (Japan)

We consider two quantization approaches to the Bateman oscillator model. One is Feshbach–Tikochinsky’s quantization approach reformulated concisely without invoking the 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.

• OSTI ID: 22852394
• Journal Information: Annals of Physics, Vol. 403; Other Information: © 2019 Elsevier Inc. 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
EIGENVECTORS
ENERGY SPECTRA
HAMILTONIANS
LIE GROUPS
OSCILLATORS
QUANTIZATION
SCALING