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International Journal of Theoretical Physics

The Infinite Square Well with a Singular Perturbation

Manuel Gadella, M. L. Glasser, Luis Miguel Nieto

Published Jan 26, 2011• 20 citations
Publisher
DOI
10.1007/s10773-011-0690-5

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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.