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Full-Text Articles in Physics
Potentials With Two Shifted Sets Of Equally Spaced Eigenvalues And Their Calogero Spectrum, Asim Gangopadhyaya, Uday P. Sukhatme
Potentials With Two Shifted Sets Of Equally Spaced Eigenvalues And Their Calogero Spectrum, Asim Gangopadhyaya, Uday P. Sukhatme
Physics: Faculty Publications and Other Works
Motivated by the concept of shape invariance in supersymmetric quantum mechanics, we obtain potentials whose spectrum consists of two shifted sets of equally spaced energy levels. These potentials are similar to the Calogero-Sutherland model except the singular term αx−2 always falls in the transition region -1/4 < a < 3/4 and there is a δ-function singularity at x=0.
Noncentral Potentials And Spherical Harmonics Using Supersymmetry And Shape Invariance, Ranabir Dutt, Asim Gangopadhyaya, Uday P. Sukhatne
Noncentral Potentials And Spherical Harmonics Using Supersymmetry And Shape Invariance, Ranabir Dutt, Asim Gangopadhyaya, Uday P. Sukhatne
Physics: Faculty Publications and Other Works
It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be applied to several problems with noncentral vector and scalar potentials. As examples, we analyze the bound state spectra of an electron in a Coulomb plus an Aharonov – Bohm field and/or in the magnetic field of a Dirac monopole.