  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 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.
