Two quantization approaches to the Bateman oscillator model

Shinichi Deguchi; Yuki Fujiwara; Kunihiko Nakano

doi:10.1016/j.aop.2019.02.004

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arXiv · 1807.04403

Two quantization approaches to the Bateman oscillator model

Shinichi Deguchi·Yuki Fujiwara·Kunihiko Nakano

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Abstract

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.

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Shinichi Deguchi, Yuki Fujiwara, Kunihiko Nakano. 2019-02-13. Two quantization approaches to the Bateman oscillator model. https://doi.org/10.1016/j.aop.2019.02.004

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