dorsal/arxiv
View SchemaQuantum damped oscillator II: Bateman's Hamiltonian vs. 2D Parabolic Potential Barrier
| Authors | Dariusz Chruscinski |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506091 |
| URL | https://arxiv.org/abs/quant-ph/0506091 |
| DOI | 10.1016/j.aop.2005.11.005 |
| Journal | Ann. Phys. 321 (2006) 840-853 |
Abstract
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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"abstract": "We show that quantum Bateman\u0027s system which arises in the quantization of a\ndamped harmonic oscillator is equivalent to a quantum problem with 2D parabolic\npotential barrier known also as 2D inverted isotropic oscillator. It turns out\nthat this system displays the family of complex eigenvalues corresponding to\nthe poles of analytical continuation of the resolvent operator to the complex\nenergy plane. It is shown that this representation is more suitable than the\nhyperbolic one used recently by Blasone and Jizba.",
"arxiv_id": "quant-ph/0506091",
"authors": [
"Dariusz Chruscinski"
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"doi": "10.1016/j.aop.2005.11.005",
"journal_ref": "Ann. Phys. 321 (2006) 840-853",
"title": "Quantum damped oscillator II: Bateman\u0027s Hamiltonian vs. 2D Parabolic Potential Barrier",
"url": "https://arxiv.org/abs/quant-ph/0506091"
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