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Full-Text Articles in Physical Sciences and Mathematics
Shape Invariance And The Exactness Of Quantum Hamilton-Jacobi Formalism, Charles Cherqui, Yevgeny Binder, Asim Gangopadhyaya
Shape Invariance And The Exactness Of Quantum Hamilton-Jacobi Formalism, Charles Cherqui, Yevgeny Binder, Asim Gangopadhyaya
Physics: Faculty Publications and Other Works
Quantum Hamilton-Jacobi Theory and supersymmetric quantum mechanics (SUSYQM) are two parallel methods to determine the spectra of a quantum mechanical systems without solving the Schr ̈odinger equation. It was recently shown that the shape invariance, which is an integrability condition in SUSYQM formalism, can be utilized to develop an iterative algorithm to determine the quantum momentum functions. In this paper, we show that shape invariance also suffices to determine the eigenvalues in Quantum Hamilton-Jacobi Theory.
Shape Invariance In Supersymmetric Quantum Mechanics And Its Application To Selected Special Functions Of Modern Physics, Chad Husko, Brenton Knuffman, Asim Gangopadhyaya, Jeffrey Mallow
Shape Invariance In Supersymmetric Quantum Mechanics And Its Application To Selected Special Functions Of Modern Physics, Chad Husko, Brenton Knuffman, Asim Gangopadhyaya, Jeffrey Mallow
Physics: Faculty Publications and Other Works
We applied the methods of supersymmetric quantum mechanics to differential equations that generate well-known special functions of modern physics. This application provides new insight into these functions and generates recursion relations among them. Some of these recursion relations are apparently new (or forgotten), as they are not available in commonly used texts and handbooks. This method can be easily extended to explore other special functions of modern physics.
Exactly Solvable Systems And The Quantum Hamilton Jacobi Formalism, C. Rasinariu, John J. Dykla, Asim Gangopadhyaya, Jeffrey Mallow
Exactly Solvable Systems And The Quantum Hamilton Jacobi Formalism, C. Rasinariu, John J. Dykla, Asim Gangopadhyaya, Jeffrey Mallow
Physics: Faculty Publications and Other Works
We connect Quantum Hamilton-Jacobi Theory with supersymmetric quantum mechanics (SUSYQM). We show that the shape invariance, which is an integrability condition of SUSYQM, translates into fractional linear relations among the quantum momentum functions.
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.
Quantum Mechanics Of Multi-Prong Potentials, Asim Gangopadhyaya, A Pagnamenta, Uday P. Sukhatme
Quantum Mechanics Of Multi-Prong Potentials, Asim Gangopadhyaya, A Pagnamenta, Uday P. Sukhatme
Physics: Faculty Publications and Other Works
We describe the bound state and scattering properties of a quantum mechanical particle in a scalar N-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy levels for the special case of N identical prongs exhibit an alternating pattern of non-degeneracy and (N−1) fold degeneracy. It is shown that the techniques of supersymmetric quantum mechanics can be used to generate new solutions. Solutions for prongs of arbitrary lengths are developed. Discussions of tunneling in N-well potentials and of scattering for piecewise constant potentials are given. Since our treatment is …