Exact Analytical Solution of the N-dimensional Radial Schrodinger Equation with Pseudoharmonic Potential via Laplace Transform Approach and Lie algebra of Ladder Operators

Tapas Das, Altuğ Arda

Published Aug 24, 2013• 2 citations

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. Our results generalize all other previous works that done for various potential combinations in the case of lower dimensions.The Ladder operators are also constructed for the pseudoharmonic potential in N-dimensions.Lie algebra associated with these operators are studied and found that they satisfy the commutation relations for the SU(1,1) group. Finally the Casimir operator is discussed briefly.

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