Research

Areas of Research

My current research interests include topics in Supersymmetric Quantum Mechanics, Shape Invariance, Quantum Hamilton-Jacobi formalism, Exactly Solvable and Quasi-exactly Solvable problems in Quantum Mechanics, Historical research in Black-Body radiation, and Physics Education. Currently, there are several undergraduate students working with me and contributing greatly to my research projects.

Contributions

In recent years, I have contributed to the following two areas:
a) My collaborators and I have shown that all shape invariant systems have an underlying algebraic structure (equivalent to the shape invariance condition) that guarantees their solvability (1,2); and
b) we have derived an infinite set of differential equations that are equivalent to the shape-invariance condition – a difference-differential equation. Solving these equations, we showed that the list of all conventional solvable was indeed complete (3,4,5).

Publications

 

  1. The Electric Field at the Chargeless Interface Between Two Regions of Space – Robert McNees and Asim Gangopadhyaya; American Journal of Physics, 82, pp. 597, June {2014); http://dx.doi.org/10.1119/1.4867378
  2. Magnet traveling through a conducting pipe: a variation on the analytical approach – Benjamin Irvine, Matthew Kemnetz, Asim Gangopadhyaya and Thomas Ruubel; American Journal of Physics, 82, pp. 273 (2014); http://dx.doi.org/10.1119/1.4864278.
  3. Undergraduate Research -What is it? – Asim Gangopadhyaya; Proceedings of The World Conference on Physics Education 2012, Pegem Akademi, ISBN 978-605-364-658-7, February, 2014 Ankara, Turkey.
  4. Unintended consequences of imprecise Notation – an example from mechanics  – Asim Gangopadhyaya and Gordon Ramsey; American Journal of Physics, 81, pp. 313, (2013).
  5. Barn and pole paradox-revisited - Robert Cacioppo and Asim Gangopadhyaya; Phys. Educ. 47, 563 (2012) doi:10.1088/0031-9120/47/5/563
  6. Supersymmetric Quantum Mechanics and Solvable Models  – J. Bougie, Asim Gangopadhyaya, J. Mallow and C. Rasinariu; Symmetry 2012, 4, 452-473; doi:10.3390/sym4030452
  7. Exceptional orthogonal polynomials  – S Sree Ranjani, P K Panigrahi, A Khare, A K Kapoor and Asim Gangopadhyaya; Journal of Physics A: Mathematical and Theoretical 45  055210 (2012).
  8. Method for generating additive shape-invariant  – Jonathan Bougie, Asim Gangopadhyaya and Jeffry V. Mallow; Journal of Physics A: Mathematical and Theoretical 44  275307 (2011).
  9. Generation of a Complete Set of Additive Shape-Invariant Potentials from an Euler Equation  – Jonathan Bougie, Asim Gangopadhyaya  and Jeffry V. Mallow; Phys. Rev. Lett. 105 , (2010) 210402.
  10. Generating Shape Invariant Potentials Asim Gangopadhyaya  and Jeffry V. Mallow; International Journal of Mod. Phys. A 23  (2008) 4959-4978.
  11. Shape invariance and the exactness of the quantum Hamilton–Jacobi formalism  – Charles Cherqui, Yevgeny Binder, and Asim Gangopadhyaya ; Phys. Lett. A 372  (2008) 1406-1415.
  12. Exactly solvable problems of quantum mechanics and their spectrum generating algebras- A review  - Constantin Rasinariu, Jeffry V. Mallow and Asim Gangopadhyaya ; Central European Journal of Physics 5  (2007) 111-134.
  13. Exactly solvable systems and the Quantum Hamilton-Jacobi formalism  – Constantin Rasinariu, John J. Dykla, Asim Gangopadhyaya , Jeffry V. Mallow; Phys.Lett. A338 (2005) 197-202.
  14. Shape Invariance in Supersymmetric Quantum Mechanics and its Application to SelectedSpecial Functions of Modern Physics – Chad Husko, Brenton Knuman, Asim Gangopadhyaya , Jeffry V. Mallow, Published in Journal of Young Investigators, 12  (2005).
  15. Reply to “Comment on Gravitational slingshot,” by C. L. Cook [Am. J. Phys. 73 (4), 363 (2005)]  - Robert Cacioppo, John Dykla and Asim Gangopadhyaya , American Journal of Physics, 73  363-364, (2005).
  16. Gravitational slingshot  – John Dykla, Robert Cacioppo and Asim Gangopadhyaya ; American Journal of Physics, 72 , 619-621, (2004).
  17. Comment on ‘‘The hidden symmetry for a quantum system with an infinitely deep square-well potential By Shi-Hai Dong and Zhong-Qi Ma [Am. J. Phys. 70 (5) 520{521 (2002)]; Asim Gangopadhyaya , Jeffry V. Mallow.; American Journal of Physics, 71 , 182 (2003).
  18. New Solvable Singular Potentials  – Ranabir Dutt, Asim Gangopadhyaya , Constantin Rasinariu, Uday P. Sukhatme; Journal of Physics A-Mathematical & General 34(19):4129-4142, (2001).
  19. Broken supersymmetric shape invariant systems and their potential algebras  – Asim Gangopadhyaya , Jeffry V. Mallow., Uday P. Sukhatme; Physics Letters A. 283(5-6):279-284, (2001).
  20. Exact Solutions of The Schroedinger Equation: Connection Between Supersymmetric Quantum Mechanics and Spectrum Generating Algebras  – Asim Gangopadhyaya, Jeffry V. Mallow., Constantin Rasinariu, Uday P. Sukhatme; Chinese Journal of Physics. 39(2):101-121, (2001).
  21. Comment on Ideal capacitor circuits and energy conservation By K. Mita and M. Boufaida [Am. J. Phys. 67 (8), 737-739 (1999)] – Asim Gangopadhyaya  and Jeffry V. Mallow., American Journal of Physics, 68 , 670-672, (2000).
  22. Coordinate realizations of deformed Lie algebras with three generator  – Ranabir Dutt, Asim Gangopadhyaya, Constantin Rasinariu, Uday P. Sukhatme; Physical Review A. 60(5): 3482-3486, (1999).
  23. Translational shape invariance and the inherent potential algebra Asim Gangopadhyaya , Jeffry V. Mallow., Uday P. Sukhatme; Physical Review A. 58(6):4287-4292, (1998).
  24. Algebraic shape invariant models  – S. Chaturvedi, Ranabir Dutt, Asim Gangopadhyaya , Prasanta K. Panigrahi, Constantin Rasinariu, Uday P. Sukhatme; Physics Letters A. 248(2-4):109-113, (1998).
  25. Shape invariance and its connection to potential algebra   – Asim Gangopadhyaya, Jeffry V. Mallow, Uday P. Sukhatme; Supersymmetry and Integrable models, Springer, LNP 502, page 341-350. Proc. of a workshop held at Chicago, IL June 1997.
  26. Noncentral potentials and spherical harmonics using supersymmetry and shape invariance  – Ranabir Dutt, Asim Gangopadhyaya , Uday P. Sukhatme American Journal of Physics, 65  400-403, (1997).
  27. Potentials with two shifted sets of equally spaced eigenvalues and their Calogero spectrum  – Asim Gangopadhyaya and Uday P. Sukhatme; Physics Letters A. 224(1-2):5-14, (1996).
  28. Methods for generating quasi-exactly solvable potentials  – Asim Gangopadhyaya , Avinash Khare, Uday P. Sukhatme; Physics Letters A. 208(4-6):261-268, (1995).
  29. Quantum mechanics of multi-prong potentials  – Asim Gangopadhyaya , Antonio Pagnamenta, Uday P. Sukhatme; Journal of Physics A-Mathematical & General. 28(18):5331-5347, (1995).
  30. Inter-Relations of Solvable Potentials  – Asim Gangopadhyaya, Prasanta K. Panigrahi, Uday P. Sukhatme; Helvetica Physica Acta. 67(4):363-368, (1994).
  31. Analysis of inverse-square potentials using supersymmetric quantum mechanics  – Asim Gangopadhyaya, Prasanta K. Panigrahi, Uday P. Sukhatme; Journal of Physics A-Mathematical & General. 27(12):4295-4300, (1994).
  32. Thermodynamics of A Free Q-Fermion Gas  – Ranabir Dutt, Asim Gangopadhyaya , Avinash Khare, Uday P. Sukhatme; International Journal of Modern Physics A. 9(15):2687-2698, (1994).
  33. New exactly solvable Hamiltonians- Shape invariance and self-similarity  – David T. Barclay, Ranabir Dutt, Asim Gangopadhyaya , Avinash Khare, Antonio Pagnamenta, Uday P. Sukhatme; Phys. Rev. A. 48(4):2786-2797, (1993).
  34. Semiclassical approach to quantum-mechanical problems with broken supersymmetry  – Ranabir Dutt, Asim Gangopadhyaya , Avinash Khare, Antonio Pagnamenta, Uday P. Sukhatme; Physical Review A. 48(3):1845-1853, (1993).
  35. Solvable Quantum Mechanical Examples of Broken Supersymmetry  – Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, and Uday P. Sukhatme; Phys. Lett. 174A, 2854 (1993).
  36. Supersymmetry and The Tunneling Problem In An Asymmetric Double Well  – Asim Gangopadhyaya, Prasanta K. Panigrahi, and Uday P. Sukhatme; Phys. Rev. A47, 2720 (1993).
  37. Anyonic superconductivity in a modified large-U Hubbard model  – Asim Gangopadhyaya  and Prasanta K. Panigrahi; Phys. Rev. B 44, 9749 (1991).
  38. Heterotic conformal field theory and Gepner’s construction  – Darwin Chang, Asim Gangopadhyaya, Alok Kumar and Jin Wang; Phys. Rev. D 42, 2694 (1990).
  39. Renormalization Group Equations In Broken Supersymmetric Theories Using Superspace Methods  - Darwin Chang and Asim Gangopadhyaya; Phys. Rev. D 33, 1771 (1986).
  40. KL-KS Mass Difference and Supersymmetric Left-Right Symmetric Theories  – Asim Gangopadhyaya ; Phys. Rev. Lett. 54, 2203 (1985).
  41. Superspace Ward identities in supersymmetric gauge theories  – Darwin Chang and Asim Gangopadhyaya; Pramana 23, 631 (1984).
  42. Possibilities for Finite Grand Unification with N = 2 Supersymmetry  – S. Kalra, D. Chang, R.N. Mohapatra and Asim Gangopadhyaya ; Lett. 145 B, 323 (1984).