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Full-Text Articles in Physics
Building Confidence In The Dirac Δ-Function, Asim Gangopadhyaya, Constantin Rasinariu
Building Confidence In The Dirac Δ-Function, Asim Gangopadhyaya, Constantin Rasinariu
Physics: Faculty Publications and Other Works
In this note we present an example from undergraduate quantum mechanics designed to highlight the versatility of the Dirac δ-function. Namely, we compute the expectation value of the Hamiltonian of a free particle in a state described by a triangular wave function ψ(x). Since the first derivative of ψ(x) is piecewise constant, and because this Hamiltonian is proportional to the second order spatial derivative, students often end up finding the expectation value to be zero—an unphysical answer. This problem provides a pedagogical application of the Dirac δ-function. By arriving at the same result via alternate pathways, this exercise reinforces students’ …
Supersymmetric Quantum Mechanics And Solvable Models, Asim Gangopadhyaya, Jonathan Bougie, Jeffrey Mallow, C. Rasinariu
Supersymmetric Quantum Mechanics And Solvable Models, Asim Gangopadhyaya, Jonathan Bougie, Jeffrey Mallow, C. Rasinariu
Physics: Faculty Publications and Other Works
We review solvable models within the framework of supersymmetric quantum mechanics (SUSYQM). In SUSYQM, the shape invariance condition insures solvability of quantum mechanical problems. We review shape invariance and its connection to a consequent potential algebra. The additive shape invariance condition is specified by a difference-differential equation; we show that this equation is equivalent to an infinite set of partial differential equations. Solving these equations, we show that the known list of h-independent superpotentials is complete. We then describe how these equations could be extended to include superpotentials that do depend on h.
Inter-Relations Of Solvable Potentials, Asim Gangopadhyaya, Prasanta K. Panigrahi, Uday P. Sukhatne
Inter-Relations Of Solvable Potentials, Asim Gangopadhyaya, Prasanta K. Panigrahi, Uday P. Sukhatne
Physics: Faculty Publications and Other Works
Solvable Natanzon potentials in nonrelativistic quantum mechanics are known to group into two disjoint classes depending on whether the Schrödinger equation can be reduced to a hypergeometric or a confluent hypergeometric equation. All the potentials within each class are connected via point canonical transformations. We establish a connection between the two classes with appropriate limiting procedures and redefinition of parameters, thereby inter-relating all known solvable potentials.