The quantum mechanics of inverse square potentials in one dimension is usually studied through renormalization, self-adjoint extension and WKB approximation. This paper shows that such potentials may be investigated within the framework of the position-dependent mass quantum mechanics formalism under the usual boundary conditions. As a result, exact discrete bound state solutions are expressed in terms of associated Laguerre polynomials with negative energy spectrum using the Nikiforov-Uvarov method for the repulsive inverse square potential.
Comments: 10 pages
[v1] 2017-03-11 05:42:37
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