### 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 G_{0} and its further extension G̃_{0} will be shown to define the phase space relevant to the problem by choosing an appropriate orbit of the coadjoint representation of G̃_{0}. 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 language | English |
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Pages (from-to) | 3139-3151 |

Number of pages | 13 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 34 |

Issue number | 14 |

DOIs | |

Publication status | Published - Apr 13 2001 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*34*(14), 3139-3151. https://doi.org/10.1088/0305-4470/34/14/318

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

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 34, no. 14, pp. 3139-3151. https://doi.org/10.1088/0305-4470/34/14/318

}

TY - JOUR

T1 - Coherent states and the role of the affine group in the quantum mechanics of the Morse potential

AU - Molnár, B.

AU - Benedict, M.

AU - Bertrand, J.

PY - 2001/4/13

Y1 - 2001/4/13

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035853664&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035853664&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/34/14/318

DO - 10.1088/0305-4470/34/14/318

M3 - Article

AN - SCOPUS:0035853664

VL - 34

SP - 3139

EP - 3151

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 14

ER -