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American Journal of Physics

Discontinuity in the first derivative of the Schrödinger wave function

Dipankar Home, S. Sengupta

Published Jun 1, 1982• 7 citations
Publisher

Abstract

Bound state problems in quantum mechanics are considered for the edge of a square well potential and singular points of a Coulomb and a δ-function potential. (AIP)
DOI
10.1119/1.12821

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This paper discusses some one dimensional quantum models with singular perturbations. Eventually, a mass discontinuity is added at the points that support the singular perturbations. The simplest model includes an attractive singular potential with a mass jump both located at the origin. We study the form of the only bound state. Another model exhibits a hard core at the origin plus one or more repulsive deltas with mass jumps at the points supporting these deltas. We study the location and the multiplicity of these resonances for the case of one or two deltas and settle the basis for a generalization. Finally, we consider the harmonic oscillator and the infinite square well plus a singular potential at the origin. We see how the energy of bound states is affected by the singular perturbation.