Spectral study of some problems in quantum mechanics

Abstract

In this thesis, we resolved Schrӧdinger equation spectral problem, for few central potentials, a single potential is the sum of the generalized Cornell potential plus an exponential potential, in the framework of quasi-exactly solvable problems. The exponential potentials that were treated are : Morse potential, the generalized Pӧschl-Teller potential, Yukawa class potential, Schiӧberg potential and Manning-Rosen potential. After inserting the central potential in the radial equation, the effective potential became a combination of terms that made the resolution of the radial equation not trivial to find, for this purpose, an approximation scheme was used to transform the radial equation into the normal form of biconfluent Heun’s equation, where the solutions are known, hence the approximate bound states of Schrӧdinger equation and their energy eigenvalues are btained in explicit form. At the end, for given values of the parameters, some of the approximate bound states and their energy levels were given.