Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D Parabolic Potential Barrier

Details Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D Parabolic Potential Barrier Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D Parabolic Potential Barrier

2005-06-11

arxiv.org/abs/quant-ph/0506091v1

Ann. Phys. 321 (2006) 840-853

Physics

Quantum Physics

15 pages

Scientific paper

10.1016/j.aop.2005.11.005

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.

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