NEW SHAPE-INVARIANT POTENTIALS IN SUPERSYMMETRIC QUANTUM-MECHANICS

Quantum mechanical potentials satisfying the property of shape invaria nce are well known to be algebraically solvable. Using a scaling ansat z for the change of parameters, we obtain a large class of new shape-i nvariant potentials which are reflectionless and possess an infinite n umber of bound states. They can be viewed as q-deformations of the sin gle soliton solution corresponding to the Rosen-Morse potential. Expli cit expressions for energy eigenvalues, eigenfunctions and transmissio n coefficicnts are given. Included in our potentials as a special case is the self-similar potential recently discussed by Shabat and Spirid onov.