DEFORMED CONFORMAL AND SUPERSYMMETRIC QUANTUM-MECHANICS

Within the standard quantum mechanics a q-deformation of the simplest N = 2 super-symmetry 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 q2-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.