111 citations · 267 across the 14 of their papers we have counts for
14 papers
Recent Advances in Semiclassical Methods Inspired by Supersymmetric Quantum Mechanics
Asim Gangopadhyaya, Jonathan Bougie, Constantin Rasinariu
Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these m…
Comments on "Numerical study of the SWKB condition of novel classes of exactly solvable systems''
Jonathan Bougie, Asim Gangopadhyaya, Constantin Rasinariu
We comment on the paper ``Numerical study of the SWKB condition of novel classes of exactly solvable systems'' [Y. Nasuda and N. Sawado, Mod. Phys. Lett. A 36, 2150025 (2021)]. We…
Generalized Langer Correction and the Exactness of WKB for all Conventional Potentials
Asim Gangopadhyaya, Jonathan Bougie, Constantin Rasinariu
In this paper we investigate the exactness of the WKB quantization condition for translationally shape invariant systems. In particular, using the formalism of supersymmetric quant…
Exactness of Semiclassical Quantization Rule for Broken Supersymmetry
Asim Gangopadhyaya, Jonathan Bougie, Constantin Rasinariu
Semiclassical methods provide important tools for approximating solutions in quantum mechanics. In several cases these methods are intriguingly exact rather than approximate, as ha…
Exactness of SWKB for Shape Invariant Potentials
Asim Gangopadhyaya, Jeffry V. Mallow, Constantin Rasinariu +1
The supersymmetry based semiclassical method (SWKB) is known to produce exact spectra for conventional shape invariant potentials. In this paper we prove that this exactness follow…
Conservation laws and energy transformations in a class of common physics problems
Jonathan Bougie, Asim Gangopadhyaya
We analyze a category of problems that is of interest in many physical situations, including those encountered in introductory physics classes: systems with two well-delineated par…
Inter-relations between additive shape invariant superpotentials
Jeffry V. Mallow, Asim Gangopadhyaya, Jonathan Bougie +1
All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on , a…
A First-Year Research Experience: The Freshman Project in Physics at Loyola University Chicago
Jonathan Bougie, Asim Gangopadhyaya, Sherita Moses +3
Undergraduate research has become an essential mode of engaging and retaining students in physics. At Loyola University Chicago, first-year physics students have been participating…
The Supersymmetric WKB Formalism is Not Exact for All Additive Shape Invariant Potentials
Jonathan Bougie, Asim Gangopadhyaya, Constantin Rasinariu
Following the verification of the conjecture made by Comtet, Bandrauk and Campbell that the supersymmetry-inspired semiclassical method known as SWKB is exact for the conventional…
Generation of a Novel Exactly Solvable Potential
Jonathan Bougie, Asim Gangopadhyaya, Jeffry V. Mallow +1
We report a new shape invariant (SI) isospectral extension of the Morse potential. Previous investigations have shown that the list of "conventional" SI superpotentials that do not…
Time Dependence and Density Inversion in Simulations of Vertically Oscillated Granular Layers
J. Bougie, Veronica Policht, Jennifer Kreft Pearce
We study a layer of grains atop a plate which oscillates sinusoidally in the direction of gravity, using three-dimensional, time-dependent numerical solutions of continuum equation…
Method for Generating Additive Shape Invariant Potentials from an Euler Equation
Jonathan Bougie, Asim Gangopadhyaya, Jeffry V. Mallow
In the supersymmetric quantum mechanics formalism, the shape invariance condition provides a sufficient constraint to make a quantum mechanical problem solvable; i.e., we can deter…
Generation of a Complete Set of Supersymmetric Shape Invariant Potentials from an Euler Equation
Jonathan Bougie, Asim Gangopadhyaya, Jeffry V. Mallow
In supersymmetric quantum mechanics, shape invariance is a sufficient condition for solvability. We show that all conventional additive shape invariant superpotentials that are ind…
Shocks in Vertically Oscillated Granular Layers
J. Bougie, Sung Joon Moon, J. B. Swift +1
We study shock formation in vertically oscillated granular layers, using both molecular dynamics simulations and numerical solutions of continuum equations to Navier-Stokes order.…