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The second order $N$-dimensional Schr\"odinger equation with pseudoharmonicpotential is reduced to a first order differential equation by using theLaplace transform approach and exact bound state solutions are obtained usingconvolution theorem. Some special cases are verified and variation of energyeigenvalues $E_n$ as a function of dimension $N$ are furnished. To give anextra depth of this letter, present approach is also briefly investigated forgeneralized Morse potential as an example.

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

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