Exact Analytical Solution of the N-dimensional Radial Schrodinger Equation with Pseudoharmonic Potential via Laplace Transform Approach

Abstract

The second order $N$-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 variation of energy eigenvalues $E_n$ as a function of dimension $N$ are furnished. To give an extra depth of this letter, present approach is also briefly investigated for generalized Morse potential as an example.

16 pages.Published version has some figures

References in corpus (8)

• Exact solutions of the modified Kratzer potential plus ring-shaped potential in the D-dimensional Schrodinger equation by the Nikiforov-Uvarov method
• Exact Solutions of the Schrödinger Equation via Laplace Transform Approach: Pseudoharmonic potential and Mie-type potentials
• An alternative simple solution of the sextic anharmonic oscillator and perturbed Coulomb problems
• A Laplace transform approach to the quantum harmonic oscillator
• Solutions of N-dimensional Schrödinger Equation with Morse Potential Via Laplace Transforms
• A Laplace transform approach to find the exact solution of the N-dimensional Schrödinger equation with Mie-type potentials and construction of Ladder operators
• The su(1,1) dynamical algebra from the Schrödinger ladder operators for N-dimensional systems: hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator
• Bound states in a double delta potential via Laplace transform

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