Generating Exactly solvable Potential using Green's function technique

In this Book we have presented a number of different new classes of exactly solvable quantum systems in non relativistic quantum mechanics applying a scheme called the Extended transformation (ET) method, in any arbitrary D-dimensional Euclidean spaces, within the framework of Green s function technique. The procedure to apply ET is to select a potential term(s) of the original potential termed as the working potential . The working potential eventually specifies the form of the basic transformation function, with the use of which the ET method is implemented. In case of multi-term potential the transformation procedure may be applied repeatedly, by selecting working potential differently to generate a variety of solved quantum system, the number of solvable quantum system in principle, being equal to the number of ways (2^n-1). A major complication that always arise dealing with non-power low potential is that the newly generated QSs are always of a Sturmian type. It behaves like a system index enumerating different QSs having a single bound state. As no standard procedure to convert Sturmian QSs to normal QSs exists, sometimes we have to use case specific regrouping techniques.

Autorentext

Name: Dr. Nilamoni Saikia,M Sc, Ph D, Guahati University, IndiaDesignation :Associte ProfessorInstitution :Chaiduar College, Gohpur-784168,IndiaGuest faculty: Rajiv Gandhi University, IndiaPublications: IOP Physica Scripta-3, Theor-Math Physics-2, Turkey J. of Physics-1,LAJPE-1, Bulgerian J. of Physics-1, Int. J of pure and Applied Physics-1,