Regarding Nonstationary Quadratic Quantum Systems
Sh. M. Nagiyev, A. I. Ahmadov, V. A. Tarverdiyeva, Sh. A. Amirova
Российский физический журнал
https://doi.org/10.1007/s11182-019-01654-7
With the help of the evolution operator method, we have established unitary connection between quadratic systems, namely between a free particle with variable mass M(t) , a particle with variable mass M(t) in a variable homogeneous field, and a harmonic oscillator with variable mass M(t) and frequency ω(t) , on which a variable force F(t) acts. Knowledge of the unitary connection allowed us to express easily in general form the propagators, invariants, wave functions, and other functions of a linear potential and a harmonic oscillator in terms of the corresponding quantities for a free particle. We have analyzed the linear and quadratic invariants in detail. Results known in the literature follow as particular cases from the general results obtained here.
- Institute of Physics of the National Academy of Sciences of Azerbaijan, Baku, AzerbaijanSh. M. Nagiyev, V. A. Tarverdiyeva & Sh. A. Amirova
- Baku State University, Baku, AzerbaijanA. I. Ahmadov
- V. G. Bagrov, D. M. Gitman, and A. S. Pereira, Usp. Fiz. Nauk, 184, No. 9, 961–966 (2014).
- Sh. M. Nagiyev, Teor. Mat. Fiz., 194, No. 2, 364–380 (2018).
- M. V. Berry and N. L. Balazs, Am. J. Phys., 47, No. 3, 264–267 (1979).
- V. V. Dodonov, V. I. Manko, and O. V. Shakhmistova, Phys. Lett. A, 102, No. 7, 295–297 (1984).
- I. Guedes, Phys. Rev. A, 63, No. 3, 034102 (2001).
- M. Feng, Phys. Rev. A, 64, No. 3, 034101 (2002).
- P.-G. Luan and C.-S. Tang, Phys. Rev. A, 71, No. 1, 014101 (2005); arXiv:quant-ph/0309174.
- K. Husimi, Progr. Theor. Phys., 9, 381–402 (1953).
- R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York (1965).
- V. S. Popov and A. M. Perelomov, Zh. Eksp. Teor. Fiz., 56, No. 4, 1375–1390 (1969).
- А. R. Lewis and W. B. Riesenfeld, J. Math. Phys., 12, 2040–2043 (1971).
- V. V. Dodonov and V. I. Man’ko, in: Proc. P. N. Lebedev Physical Institute of the Academy of Sciences, Vol. 183 (1987), p.182.
- I. A. Pedrosa, Phys. Rev. A, 55, No. 4, 3219–3221 (1997).
- R. Cordero-Soto, E. Suazo, and S. K. Suslov, Ann. Phys., 325, 1884–1912 (2010).
- K. H. Yeon, H. Ju. Kim, C. I. Um, et al., Phys. Rev. A, 50, No. 2, 1035–1039 (1994).
- D.-Y. Song, J. Phys. A, 32, 3449–3456 (1999).
- P. Camiz, A. Gerardi, C. Marchioro, et al., J. Math., 12, 2040–2043 (1971).
- Sh. M. Nagiyev and K. Sh. Jafarova, Phys. Lett. A, 377, No. 10–11, 747–752 (2013).
- Sh. M. Nagiyev, Teor. Mat. Fiz., 188, No. 1, 76–84 (2016).
- V. G. Bagrov, D. M. Gitman, I. M. Ternov, et al., Exact Solutions of Relativistic Wave Equations [in Russian], Nauka, Novosibirsk (1982).
- V. G. Bagrov, Russ. Phys. J., 61, No. 3, 403–411 (2018).
- V. G. Bagrov, A. V. Shapovalov, and I. V. Shirokov, Teor. Mat. Fiz., 87, No. 3, 426–433 (1991).
- V. G. Bagrov, A. V. Shapovalov, and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved. Fiz., 32, No. 11, 112–114 (1989).
- I. A. Malkin and V. I. Man’ko. Dynamical Symmetries and Coherent States of Quantum Systems [in Russian], Nauka, Moscow (1979).
- G. Schrade, V. I. Manko, W. P. Schleich, and R. J. Glauber, Quantum Semiclass. Opt., 7, 307–325 (1995).
- O. Castanos, S. Hacyan, R. Lopez-Pena, and V. I. Manko, J. Phys. A, 31, 1227 (1998).
- A. M. Perelomov and V. S. Popov, Teor. Mat. Fiz., 3, No. 3, 377–391 (1970).
- F. J. Dyson, Phys. Rev., 75, No. 1, 1736–1755 (1949).
- A. R. P. Rau and K. Unnikrishan, Phys. Lett. A, 222, 304–308 (1996).