Transformation Formalism of Generation of New Exactly Solvable Quantum Potential Systems

Abstract

Extended transformation method is applied to find exactly solvable general quantum mechanical potential system. Exact bound state eigenvalues and Eigen functions of the Schrödinger equation for specific potentials are obtained in any chosen dimensional space, using extended transformation (ET) method which may find applications in different branches of Physics. We have found for multiterm power law potentials, under the framework of ET that a family relationship emerges among the parent and the newly generated exactly solvable potentials (ESPs). The normalizability of bound state solutions of the generated quantum systems is also discussed.