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Full-Text Articles in Physics
Exact Solutions Of The Schroedinger Equation: Connection Between Supersymmetric Quantum Mechanics And Spectrum Generating Algebras, Asim Gangopadhyaya, Jeffrey Mallow, C. Rasinariu, Uday P. Sukhatne
Exact Solutions Of The Schroedinger Equation: Connection Between Supersymmetric Quantum Mechanics And Spectrum Generating Algebras, Asim Gangopadhyaya, Jeffrey Mallow, C. Rasinariu, Uday P. Sukhatne
Physics: Faculty Publications and Other Works
Using supersymmetric quantum mechanics, one can obtain analytic expressions for the eigenvalues and eigenfunctions for all nonrelativistic shape invariant Hamiltonians. These Hamiltonians also possess spectrum generating algebras and are hence solvable by an independent, group theoretical method. In this paper, we demonstrate the equivalence of the two methods of solution, and review related progress in this field.
Broken Supersymmetric Shape Invariant Systems And Their Potential Algebras, Asim Gangopadhyaya, Jeffrey Mallow, Uday P. Sukhatne
Broken Supersymmetric Shape Invariant Systems And Their Potential Algebras, Asim Gangopadhyaya, Jeffrey Mallow, Uday P. Sukhatne
Physics: Faculty Publications and Other Works
Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentials correspond to broken supersymmetry, since there is no zero energy eigenstate. We describe a novel two-step shape invariance approach as well as a group theoretic potential algebra approach for solving such broken supersymmetry problems.
New Solvable Singular Potentials , R. Dutt, Asim Gangopadhyaya, C. Rasinariu, Uday P. Sukhatne
New Solvable Singular Potentials , R. Dutt, Asim Gangopadhyaya, C. Rasinariu, Uday P. Sukhatne
Physics: Faculty Publications and Other Works
We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, Pöschl-Teller I and Pöschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special care to regularize the inverse square singularity at the origin. The regularization procedure gives rise to a delta-function behavior at the origin. Our new systems possess underlying non-linear potential algebras, which can also be used to determine their spectra analytically.