Quantum Feature Of Branched Hamiltonians

Dibyendu Ghosh

Authors

Dibyendu Ghosh Department of Mathematics, Barrackpore R. S. N College,Barrackpore, Kolkata-700120, India https://orcid.org/0009-0004-9722-9203

Keywords:

Hamiltonian , Multi-valued , Liénard oscillator , Quantum , Momentum dependent mass

Abstract

We point out that a quadratic Liénard-type equation, when appropriately interpreted, exhibits branching behavior as a consequence of the double-valued nature of its governing Hamiltonian. Under a suitable approximation involving the coupling constant, we derive the corresponding quantum mechanical model, which is characterized by a momentum-dependent effective mass function.

Downloads

Download data is not yet available.

References

C. M. Bender, P. E. Dorey, C. Dunning, A. Fring, D. W. Hook, H. F. Jones, S. Kuzhel, G. Levai, and R. Tateo, PJ Symmetry: In Quantum and Classical Physics, World Scientific, Singapore.

B. P. Mandal, B. K. Mourya, K. Ali and A. Ghatak, Ann. Phys. 363, 185 (2015).

A. Shapere and F. Wilczek, Phys. Rev. Lett. 109, 200402 (2012).

A. Shapere and F. Wilczek, Phys. Rev. Lett. 109, 160402 (2012).

F. Wilczek, Phys. Rev. Lett. 109, 160401 (2012).

M. Henneanx, C. Teitelboim and J. Zanelli, Phys. Rev. A 36, 4417 (1987).

T. L. Curtright and C. K. Zachos, J. Phys. A 42, 485208 (2009).

T. L. Curtright and C. K. Zachos, J. Phys. A 43, 445101 (2010).

T.L. Curtright and A. Veitia, Phys. Lett. A 375, 276 (2011).

T.L. Curtright, SIGMA 7, 042 (2011).

T. L. Curtright and C. K. Zachos, J. Phys. A: Math. Theor. 47, 145201 (2014).

T. L. Curtright, Bulg. J. Phys. 45, 102 (2018).

B. Bagchi, S. Modak, P. K. Panigrahi, F. Ruzicka and M. Znojil, Mod. Phys. Lett. A 30, 1550213 (2015).

B. Bagchi, S. M. Kamil, T. R. Tummuru, I. Semoradova and M. Znojil, J. Phys.: Conf. Series 839, 012011 (2017).

A. Ghose-Choudhury and P. Guha, Mod. Phys. Lett. A 34, 1950263 (2019).

F. Bagarello, J. P. Gazeau, F. H. Szafraniec and M. Znojil, editors, (2015) NonSelfadjoint Operators in Quantum Physics: Mathematical Aspects, John Wiley Sons.

M. Znojil, J. Phys. A: Math. Theor. 48, 195303 (2015).

M. Znojil and G. Levai, Phys. Lett. A 376, 3000 (2012).

C. Quesne and V. M. Tkachuk, J. Phys. A: Math. Gen. 37, 4267 (2004).

B. Bagchi, A. Banerjee, C. Quesne and V. M. Tkachuk, J. Phys. A: Math. Gen. 38, 2929 (2005).

B. Bagchi and T. Tanaka, Phys. Lett. A 372, 5390 (2008).

T. L. Curtright, D. B. Fairlie, and C. K. Zachos, (2014) A Concise Treatise on Quantum Mechanics in Phase Space, Imperial College and World Scientific Press; (ISBN 978-981-4520-43-0).

E. Witten, Nucl. Phys. B 188, 513 (1981).

E. Witten, Nucl. Phys. B 202, 253 (1982).

F. Cooper, A. Khare and U. Sukhatme, Phys. Rep. 251, 267 (1995).

B Bagchi, (2000) Supersymmetry in Quantum and Classical Mechanics, Chapman and Hall/CRC.

M. Znojil, J. Phys. A: Math. Gen 35, 2341 (2002).

B. Bagchi, D. Ghosh and T. R. Tummuru, J. Non. Evol. Eqns and Appl. 2018, 101 (2020).

B. Bagchi, A. Ghose Choudhury and P. Guha, J. Math. Phys. 56, 012105 (2015).

B. Bagchi, R. Ghosh and P. Goswami, J. Phys: Conf. Ser. 1540, 012004 (2020).

A. Liénard, Revue générale de l'électricité 23, 901 (1928).

A. Liénard, Revue générale de l'électricité 23, 946 (1928).

M. Lakshmanan and S. Rajasekar, (2013) Nonlinear dynamics: Integrability chaos and patterns, Springer-Verlag, New York.

V. Chithiika Ruby, M. Senthivelan and M. Lakshmanan, J. Phys. A: Math. Theor. 45, 382002 (2012).