Exact Analytical Solution of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>-Dimensional Radial Schrödinger Equation with Pseudoharmonic Potential via Laplace Transform Approach

Abstract

The second-order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>-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 eigenvalues<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>as a function of dimension<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>are furnished. To give an extra depth of this paper, the present approach is also briefly investigated for generalized Morse potential as an example.