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

Abstract

The second order N-dimensional Schrodinger equation with Mie-type potentials is reduced to a first order differential equation by using the Laplace transformation. Exact bound state solutions are obtained using convolution or Faltungs theorem. The Ladder operators are also constructed for the Mie-type potentials in N- dimensions. Lie algebra associated with these operators are studied and it is found that they satisfy the commutation relations for the SU(1,1) group.

12 pages

References in corpus (5)

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Cited by in corpus (4)

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• Time independent fractional Schrodinger equation for generalized Mie-type potential in higher dimension framed with Jumarie type fractional derivative
• Analytical approximate bound state solution of Schrödinger equation in $D$-dimensions with a new mixed class of potential for arbitrary $\ell$-state via asymptotic iteration method
• Klein-Gordon equation for a charged particle in space varying electromagnetic fields-A systematic study via Laplace transform