Exact Analytical Solution Of The N-Dimensional Radial Schrodinger Equation With Pseudoharmonic Potential Via Laplace Transform Approach

Abstract

The second-order N-dimensional Schrodinger equation with pseudoharmonic potential is reduced to a first-order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution theorem. Some special cases are verified and variations of energy eigenvalues E-n as a function of dimension N are furnished. To give an extra depth of this paper, the present approach is also briefly investigated for generalized Morse potential as an example.