Intrinsic resonance representation of quantum mechanics

M. Carioli, E.J. Heller, Klaus Braagaard Møller

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Abstract

The choice of basis states in quantum calculations can be influenced by several requirements, and sometimes a very natural basis suggests itself. However often one retreats to a ''merely complete'' basis, whose coefficients in the eigenstates carry Little physical insight. We suggest here an optimal representation, based purely on classical mechanics. ''Hidden'' constants of the motion and good actions already known to the classical mechanics are thus incorporated into the basis, leaving the quantum effects to be isolated and included by small matrix diagonalizations. This simplifies the hierarchical structure of couplings between ''zero-order'' states. We present a (non-perturbative) method to obtain such a basis-state as solutions to a certain resonant Hamilton-Jacobi equation. (C) 1997 American Institute of Physics.
Original languageEnglish
JournalJournal of Chemical Physics
Volume106
Issue number20
Pages (from-to)8564-8571
ISSN0021-9606
DOIs
Publication statusPublished - 1997

Bibliographical note

Copyright (1997) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

Keywords

  • GUSTAVSON NORMAL-FORM
  • HAMILTON-JACOBI EQUATION
  • SEMI-CLASSICAL QUANTIZATION
  • ENERGY-LEVELS
  • NONSEPARABLE SYSTEMS
  • PERTURBATION-THEORY
  • APPROXIMATE CONSTANTS
  • INVARIANT TORI
  • ALGEBRAIC QUANTIZATION
  • SEMICLASSICAL QUANTIZATION

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