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Full-Text Articles in Physics

New Exactly Solvable Hamiltonians - Shape Invariance And Self-Similarity, David T. Barclay, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday P. Sukhatne Oct 1993

New Exactly Solvable Hamiltonians - Shape Invariance And Self-Similarity, David T. Barclay, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday P. Sukhatne

Physics: Faculty Publications and Other Works

We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission ...


Semiclassical Approach To Quantum-Mechanical Problems With Broken Supersymmetry, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday P. Sukhatne Sep 1993

Semiclassical Approach To Quantum-Mechanical Problems With Broken Supersymmetry, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday P. Sukhatne

Physics: Faculty Publications and Other Works

The semiclassical WKB approximation method is reexamined in the context of nonrelativistic quantum-mechanical bound-state problems with broken supersymmetry (SUSY). This gives rise to an alternative quantization condition (denoted by BSWKB) which is different from the standard WKB formula and also different from the previously studied supersymmetric (SWKB) formula for unbroken SUSY. It is shown that to leading order in ħ, the BSWKB condition yields exact energy eigenvalues for shape-invariant potentials with broken SUSY (harmonic oscillator, Pöschl-Teller I and II) which are known to be analytically solvable. Further, we show explicitly that the higher-order corrections to these energy eigenvalues, up to ...


Supersymmetry And The Tunneling Problem In An Asymmetric Double Well, Asim Gangopadhyaya, Prasanta K. Panigrahi, Uday P. Sukhatne Apr 1993

Supersymmetry And The Tunneling Problem In An Asymmetric Double Well, Asim Gangopadhyaya, Prasanta K. Panigrahi, Uday P. Sukhatne

Physics: Faculty Publications and Other Works

The techniques of supersymmetric quantum mechanics are applied to the calculation of the energy difference between the ground state and the first excited state of an asymmetric double well. This splitting, originating from the tunneling effect, is computed via a systematic, rapidly converging perturbation expansion. Perturbative calculations to any order can be easily carried out using a logarithmic perturbation theory. Our approach yield substantially better results than alternative widely used semiclassical analyses.