Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. 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 the q 2 -factor scaling. A special class of the self-similar potentials is shown to obey the dynamical conformal symmetry algebra su q (1,1). These potentials exhibit exponential spectra and corresponding raising and lowering operators satisfy the q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane.
No takes yet. Share an insight, caveat, or question.
V. P. Spiridonov (1992) studied this question.