Coherent states and the role of the affine group in the quantum mechanics of the Morse potential

B. Molnár, M. Benedict, J. Bertrand

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

The coherent states of the Morse potential that have been obtained earlier from supersymmetric quantum mechanics, are shown to be connected with the representations of the affine group of the real line and some of its extensions. This relation is similar to the one between the Heisenberg-Weyl group and the coherent states of the harmonic oscillator. The states that minimize the uncertainty product of the generators of the affine Lie algebra are shown to contain all the coherent states of the Morse oscillator plus the intelligent states of the Morse Hamiltonians with different shape parameter s. The representations of the central extension of the affine group denoted by G0 and its further extension G̃0 will be shown to define the phase space relevant to the problem by choosing an appropriate orbit of the coadjoint representation of G̃0. This allows one to construct a generalized Wigner function on this phase space, which is again essentially in the same relation with the affine group, as the ordinary Wigner function with the Heisenberg-Weyl group.

Original languageEnglish
Pages (from-to)3139-3151
Number of pages13
JournalJournal of Physics A: Mathematical and General
Volume34
Issue number14
DOIs
Publication statusPublished - Apr 13 2001

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Morse potential
Morse Potential
Affine Group
Quantum theory
Coherent States
Quantum Mechanics
quantum mechanics
Wigner Function
Weyl Group
Heisenberg Group
Hamiltonians
Phase Space
Algebra
Supersymmetric Quantum Mechanics
Affine Lie Algebras
Orbits
Central Extension
Shape Parameter
Generalized Functions
Harmonic Oscillator

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Coherent states and the role of the affine group in the quantum mechanics of the Morse potential. / Molnár, B.; Benedict, M.; Bertrand, J.

In: Journal of Physics A: Mathematical and General, Vol. 34, No. 14, 13.04.2001, p. 3139-3151.

Research output: Contribution to journalArticle

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