Exactly-solvable systems have a special importance in physics as not too many physical examples can be solved exactly especially in the closed form that allows a straightforward analysis of the underlying solutions. It is for this particular reason that systems like the one-dimensional Ising model hold a special place in textbooks. The search for new exactly-solvable systems is almost always interesting as it is possible that they may also be related to known exactly-solvable ones. Moreover, finding integrable systems is yet another interesting program.
I have had a keen interest in classical mechanics and dynamical systems since as an undergraduate. As a matter of fact, my initial explorations as a researcher were on one-dimensional nonlinear oscillators which lead to two publications (jointly with my supervisors and other collaborators) [1,2] in which we reported some analytical results on period functions and exact solutions of purely nonlinear oscillators (by that one means oscillators which cannot be linearized).
In the following years during graduate school, I worked on Hamiltonian systems and their first integrals. In particular, me and my collaborators investigated symmetries of harmonic as well as supersymmetric oscillators leading to conservation laws [3,4], and also explored the action-angle method in determining conserved quantities [5]. Some of these results have been extended and summarized in [6].
Coming now to quantum systems, on the one hand, me and my collaborators have explored certain non-Hermitian quantum systems with real spectra (such systems are called pseudo-Hermitian) [7,8]. On the other hand, we have investigated several exactly-solvable quantum systems belonging to the Lienard class of systems [9,10], for which the construction of the (classical) Lagrangian and Hamiltonian formalisms have been summarized in the review article [11]. The analysis has been extended to relativistic quantum mechanics as well [12].
Collaborators:
1) Bijan Bagchi (Brainware University)
2) Akash Sinha (IIT-BBS)
3) Anindya Ghose-Choudhury (Diamond Harbour Women's University)
4) Partha Guha (Khalifa University)
5) Bhabani Prasad Mandal (Banaras Hindu University)
6) Miloslav Znojil (Czech Academy of Sciences)
7) Chandrasekhar Bhamidipati (IIT-BBS)
8) Ankan Pandey (Galgotias University)
Related publications:
[1] A. Ghose-Choudhury, A. Ghosh, P. Guha, and A. Pandey, Int. J Non-Linear. Mech. 106, 55 (2018) [arXiv].
[2] A. Ghosh and C. Bhamidipati, Int. J Non-Linear. Mech. 116, 167 (2019) [arXiv].
[3] A. Sinha, A. Ghosh, and B. Bagchi, Phys. Scr. 98, 095253 (2023) [arXiv].
[4] A. Sinha, A. Ghosh, and B. Bagchi, Phys. Scr. 99, 085257 (2024) [arXiv].
[5] A. Sinha and A. Ghosh, Pramana 98, 101 (2024) [arXiv].
[6] A. Ghosh, A. Sinha, and B. Bagchi, J. Phys.: Conf. Ser. 2912, 12028 (2024) [arXiv].
[7] A. Sinha, A. Ghosh, and B. Bagchi, Phys. Scr. 99, 105534 (2024) [arXiv].
[8] A. Ghosh and A. Sinha, J. Phys.: Conf. Ser. 2986, 012004 (2025) [arXiv].
[9] B. Bagchi, A. Ghose-Choudhury, A. Ghosh, and P. Guha, arXiv:2412.09100.
[10] A. Ghosh, B. P. Mandal, and B. Bagchi, arXiv:2501.08424.
[11] B. Bagchi, A. Ghosh, and M. Znojil, Symmetry 16, 860 (2024) [arXiv].
[12] A. Ghosh and B. P. Mandal, Phys. Lett. A 545, 130488 (2025) [arXiv].