2022   04   az   p.37-42 Sh. A. Amirova,
Oscillator with a position-dependent mass in a homogeneous gravitational field: Ω²=0 and Ω²<0 cases		  pdf 

ABSTRACT

The model with a position-dependent non-relativistic quantum linear harmonic oscillator in an external homogeneous gravitational field was studied for values of the renormalized frequency Ω^2=0 and Ω^2<0 and the generalized free Hamiltonian, the corresponding Schrödinger equation was exact solved. The wave functions and energy spectrum are found. Wave functions are expressed by pseudo-Jacobi polynomials.

Keywords: Coordinate dependent mass, quantum harmonic oscillator, pseudo Jacobian polynomials, non-equidistant energy spectrum
PACS: 03.65.-w, 02.30.Hq, 03.65.Ge

DOI:-

Received: 21.11.2022

AUTHORS & AFFILIATIONS

Institute of Physics Ministry of Science and Education Republic of Azerbaijan, 131 H.Javid ave, Baku, AZ-1143, Azerbaijan
E-mail: shovqiyya@mail.ru 		REFERENCIES

[1]   Sh.M. Nagiyev, C. Aydın, A.I. Ahmadov, Sh.A. Amirova. Eur. Phys. J.Plus., 2022, 137:540
[2]   Sh. M. Nagiyev. Theor. Math. Phys. 2022, 210: 1, 121-134.
[3]   G. Bastard. Wave Mechanics Applied to Semiconductors (Les Editions de Physique, CNRS, 1988.
[4]   D.J. Ben Daneil, C. B. Duke. Phys. Rev., 152:2, 1966, 683–692.
[5]   C. Quesne and V.M. Tkachuk. J. Phys. A: Math. Gen., 2004, 37, 4267.
[6]   Shi-Hai Dong, Guo-Hua Sun. M. Lozada-Cassou. Phys. Lett. A 340, 2005, (1-4), 94-103.
[7]   E.I. Jafarov, Sh. M Nagiyev, R. Oste and J. Van der Jeugt. J. Physics A: Math.Theor. 53, 485301, 2020.
[8]   O. von Roos. Phys. Rev. B, 1983, 27, 7547.
[9]   F. Nikiforov and V.B. Uvarov. Special Functions of Mathematical Physics: A Unified Introduction with Applications (Birkhauser, Basel 1988.
[10]  R. Koekoek, P.A. Lesky and R.F. Swarttouw. Hypergeometric Orthogonal Polynomials and their q-Analogues, (Springer, Berlin 2010.
[11]  H.I. Ahmadov, C. Aydin, N.SH. Huseynova and O. Uzun. Int. J. Mod. Phys. E,vol. 22, № 10, 1350072, 2013.
[12]  E.I. Jafarov, Sh.M. Nagiyev and A.M. Jafarova. Reports Math. Phys., 2020, 86, 25.
[13]  E.I. Jafarov and S. M. Nagiyev. Mod. Phys. Lett. A 36, 2021, № 29, 2150206.
[14]  Jiang Yu, Shi-Hai Dong, Guo-Hua Sun. Physics Letters A 322(5-6), 290-297, 2004.
[15]  C. Quesne. J. Phys. A: Math. Gen. 21, 3093 1988.
[16]  E.I. Jafarov, J. Van der Jeugt. Eur. Phys. J. Plus. 2021, 136:758.
[17]  H. Rajbongshi. Theor. Math. Phys., 2015, 184, 996.
[18]  E.I. Jafarov and Sh.M. Nagiyev. Theor. Math. Phys. 207: 1, 447-458, 2021.