A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.

AIP conference proceedingsJan 1, 20120 citations

Few-Body Systems

q-deformed Quantum Mechanics with q-translation Symmetry and Supersymmetric q-deformed Quantum Mechanics

Won Sang Chung, HASSAN HASSANABADI

Published Dec 3, 2019• 3 citations

Publisher

DOI: 10.1007/s00601-019-1538-4

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Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional

N=2

supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are

q

-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by

q^2

-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a

q

-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra

su_q(1,1)

is described. Further possibilities for

q

-deformation of known solvable potentials are outlined. Talk presented at the workshop on Harmonic Oscillators, College Park, 25-28 March 1992.