WKB Energy Expression for the Radial Schrödinger Equation with a Generalized Pseudoharmonic Potential

In this paper, we applied the semi-classical quantization approximation method to solve the radial Schrödinger equation with a generalized Pseudoharmonic potential. The four turning points problem within the framework of the Wentzel-Kramers-Brillouin (WKB) method was transformed into two turning points and subsequently, the energy spectrum was obtained. Some special cases of the generalized Pseudoharmonic potential are presented. The WKB approximation approach reproduces the exact energy expression obtained with several analytical methods in the literature. The values of the energy levels for some selected diatomic molecules (N2, CO, NO, CH) obtained numerically are in excellent agreement with those from previous works in the literature.

Exact Analytical Solution of theN-Dimensional Radial Schrödinger Equation with Pseudoharmonic Potential via Laplace Transform Approach

The second-orderN-dimensional Schrödinger 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 eigenvaluesEnas a function of dimensionNare furnished. To give an extra depth of this paper, the present approach is also briefly investigated for generalized Morse potential as an example.