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Time-dependent perturbation theory with a classical limit.

Shamik Banerjee1, J K Bhattacharjee

  • 1Department of Physics, Presidency College, Kolkata-700073, India. bshamik@iitk.ac.in

Physical Review Letters
|September 28, 2004
PubMed
Summary
This summary is machine-generated.

This study introduces a new quantum mechanical perturbation theory using multiple time scales. The method smoothly transitions to classical mechanics and incorporates nonperturbative elements.

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Area of Science:

  • Quantum mechanics
  • Theoretical physics
  • Perturbation theory

Background:

  • Classical and quantum mechanics present distinct frameworks for describing physical systems.
  • Bridging the gap between quantum and classical descriptions is crucial for understanding phenomena across different scales.

Purpose of the Study:

  • To develop a novel quantum mechanical perturbation theory.
  • To integrate the multiple time scale technique into perturbation theory.
  • To ensure the theory smoothly connects with classical mechanics.

Main Methods:

  • Utilized the time translation operator.
  • Employed a variant of the Bender and Bettencourt method.
  • Incorporated the multiple time scale technique.

Main Results:

  • Developed a perturbation theory that smoothly transitions to classical results as Planck's constant approaches zero.
  • Demonstrated an inherent nonperturbative element within the developed technique.

Conclusions:

  • The new perturbation theory offers a unified approach applicable across quantum and classical regimes.
  • The technique's nonperturbative nature provides a more robust framework for certain quantum mechanical problems.