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Perturbation theory on generalized quantum mechanical systems

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  • Sudarshan, E.C.G.
  • Chiu, Charles B.
  • Bhamathi, G.

Abstract

We present a general formalism for doing the perturbation theory in the complex energy plane, where the notion of the generalized quantum mechanical systems is used. This formalism is applied to the Friedrichs-Lee model. It reproduces the results of the exact solution, where the spectrum of the generalized quantum mechanical system consists of a discrete complex energy pole and a continuum spectrum (which passes below this discrete pole) in the complex energy plane. We also investigate the role of the “complex delta” function in the description of a resonance state. The unboundedness of the spectrum appears to be the very ingredient needed to give rise to a pure exponential decay.

Suggested Citation

  • Sudarshan, E.C.G. & Chiu, Charles B. & Bhamathi, G., 1994. "Perturbation theory on generalized quantum mechanical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 202(3), pages 540-552.
    • Handle: RePEc:eee:phsmap:v:202:y:1994:i:3:p:540-552
    DOI: 10.1016/0378-4371(94)90478-2
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    References listed on IDEAS

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    1. Petrosky, T. & Prigogine, I. & Tasaki, S., 1991. "Quantum theory of non-integrable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 173(1), pages 175-242.
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