A New Method to Generating Exactly Solvable Quantum Potential : Exactly Solvable Schrodinger Equation for Mono term and multiterm Quantum mechanical potentials

This book has dealt with the generation of exact analytic bound state solution of the Schrodinger equation, taking as 'seed' an already analytically solved quantum system. The method rests on a coordinate transformation followed by a functional transformation. The former is the basic transformation and has been used in earlier treatment mapping one system into another. Earlier studies of mapping by various hors dealt with a 1-dimensional system and completely sidetracked the important question of the dimensionality of the space of the transformed system. Ealier studies on similar lines were fraught with an inaccurate specification of the angular momentum quantum number 'L' or beset with an element of ad-hocness. Within the context of the coordinate transformation and power-law potential we have studied the dimensionality aspect of the transformed quantum system and found that except when the A-system is taken in 2-dimensional space, there is always a change in the dimensionality of the B-system. The difficulty arising due to dimensional mismatch can be overcome by performing an Extenden transformation instead of the simple coordinate transformation on the original exactly solvable