Abstract
AbstractIn this work, we present an operational method based on the use of supersymmetry applied to quantum mechanics, shape invariance, and intertwining techniques to determine certain classes of solvable potentials. Our proposal uses an ansatz which matches the Witten superpotential, allowing us to identify, through a particular Ricatti relationship, the potentials that are solvable as well as to obtain straightforwardly the corresponding ground state eigenvalues, energy, and wave function. As a useful application of the proposed method, we obtain some examples of solvable quartic potentials as well as, with the aid of the standard and generalized Darboux transform, the partner isospectral potentials that are associated with the models under consideration. The method can be easily extended and used to find new solvable potentials which could be useful in the modeling of specific quantum interactions. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001
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