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The second order N-dimensional Schrodinger equation with Mie-type potentialsis reduced to a first order differential equation by using the Laplacetransformation. Exact bound state solutions are obtained using convolution orFaltungs theorem. The Ladder operators are also constructed for the Mie-typepotentials in N- dimensions. Lie algebra associated with these operators arestudied and it is found that they satisfy the commutation relations for theSU(1,1) group.

journal of mathematical chemistry

A Laplace transform approach to find the exact solution of the  N-dimensional Schr\"odinger equation with Mie-type potentials and  construction of Ladder operators