Zobrazeno 1 - 10
of 45
pro vyhledávání: '"Bougie, Jonathan"'
Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as crucial test cas
Externí odkaz:
http://arxiv.org/abs/2408.15424
Publikováno v:
Modern Physics Letters A (2023) 2375002
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 show that it misrepresents our prior work [J. Bougie, A. Gangopadhyaya
Externí odkaz:
http://arxiv.org/abs/2311.02092
In this paper we investigate the exactness of the WKB quantization condition for translationally shape invariant systems. In particular, using the formalism of supersymmetric quantum mechanics, we generalize the Langer correction and show that it gen
Externí odkaz:
http://arxiv.org/abs/2212.13118
Semiclassical methods provide important tools for approximating solutions in quantum mechanics. In several cases these methods are intriguingly exact rather than approximate, as has been shown by direct calculations on particular systems. In this pap
Externí odkaz:
http://arxiv.org/abs/2012.05053
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 follows from their additive shape invariance.
Comment: 15 pages, 2 figu
Comment: 15 pages, 2 figu
Externí odkaz:
http://arxiv.org/abs/2005.06683
Autor:
Bougie, Jonathan, Gangopadhyaya, Asim
Publikováno v:
American Journal of Physics 87, 868 (2019)
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 parts that exchange energy, eventually reaching a shared equilibrium with
Externí odkaz:
http://arxiv.org/abs/1910.13569
Publikováno v:
Physics Letters A, Volume 384, Issue 6, 28 February 2020, 126129
All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on $\hbar$, and their $\hbar$-dependent extensions. The former group themselves int
Externí odkaz:
http://arxiv.org/abs/1909.02704
Autor:
Bougie, Jonathan, Gangopadhyaya, Asim, Moses, Sherita, Polak, Robert D., Ramsey, Gordon P., Walkosz, Weronika
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 in the Freshman Projects program for over twenty years, which has coi
Externí odkaz:
http://arxiv.org/abs/1906.03302
Publikováno v:
Final version published at Journal of Physics A: Mathematical and Theoretical, J. Phys. A: Math. Theor. 51 375202 (2018)
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 additive shape invariant potentials, it was widely believed that SWKB
Externí odkaz:
http://arxiv.org/abs/1802.00068
Publikováno v:
Phys.Lett. A379 (2015) 2180-2183
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 depend explicitly on Planck's constant $\hbar$ is complete. Additiona
Externí odkaz:
http://arxiv.org/abs/1506.08809