Constants of Motion of the Harmonic Oscillator

Belmonte, Fabián; Cuéllar, Sebastián

doi:10.1007/s11040-020-09362-2

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“…Motion of the non-relativistic quantum harmonic oscillator under the suddenly exposed constant external field is an exception here. The rest of the known exactly-solvable quantum harmonic oscillator models exhibit dynamical symmetries, which belong to Lie (super)algebra or q-deformation of the Heisenberg-Weyl algebra [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

The Husimi function of a semiconfined harmonic oscillator model with a position-dependent effective mass

Jafarov

Jafarova

Nagiyev

2022

Int. J. Mod. Phys. B

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In this paper, the phase space representation for a semiconfined harmonic oscillator model with a position-dependent effective mass is constructed. We have found the Husimi distribution function for the stationary states of the oscillator model under consideration for both cases without and with the applied external homogeneous field. The obtained function is expressed through the double sum of the parabolic cylinder function. Different special cases and the limit relations are discussed, too.

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