Abstract
We extend exactly solvable model of a one-dimensional non-relativistic canonical semiconfined quantum harmonic oscillator with a mass that varies with position to the case where an external homogeneous field is applied. The problem is still exactly solvable and the analytic expression of the wave functions of the stationary states is expressed by means of generalised Laguerre polynomials, too. Unlike the case without any external field, when the energy spectrum completely overlaps with the energy spectrum of the standard non-relativistic canonical quantum harmonic oscillator, the energy spectrum is now still equidistant but depends on the semiconfinement parameter a. We also compute probabilities of the transitions for the model under the external field and discuss limit cases for the energy spectrum, wave functions and probabilities of transitions, when the semiconfinement parameter a goes to infinity.
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References
S G Joshi, J. Acoust. Soc. Am. 72, 1872 (1982)
B D Zaitsev and I E Kuznetsova, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43, 701 (1996)
W Krassowska and J C Neu, Biophys. J. 66, 1768 (1994)
M Taleb, C Didierjean, C Jelsch, J P Mangeot, B Capelle and A Aubry, J. Crystal Growth 200, 575 (1999)
T Stuyver, D Danovich, J Joy and S Shaik, WIREs Comput. Mol. Sci. e1438 (2019)
M Aschi, R Spezia, A Di Nola and A Amadei, Chem. Phys. Lett. 344, 374 (2001)
L Zhang and H-J Xie, Phys. Rev. B 68, 235315 (2003)
L Zhang and H-J Xie, Mod. Phys. Lett. B 17, 347 (2003)
L Zhang and H-J Xie, Physica E 22, 791 (2004)
K Ganesan and R Gebarowski, Pramana – J. Phys. 48, 379 (1997)
M Hosseini, H Hassanabadi and S Hassanabadi, Pramana – J. Phys. 93, 16 (2019)
F Smallenburg, H Rao Vutukuri, A Imhof, A van Blaaderen and M Dijkstra, J. Phys.: Condens. Matter 24, 464113 (2012)
Chao Zhang and Lu Huang, Physica A 389, 5769 (2010)
P Pedram, Physica A 391, 2100 (2012)
L-A Cotfas, Physica A 392, 371 (2013)
E I Jafarov and J Van der Jeugt, Eur. Phys. J. Plus 136, 758 (2021)
L D Landau and E M Lifshitz, Quantum mechanics: Non-relativistic theory (Pergamon Press, Oxford, England, 1991)
S C Bloch, Introduction to classical and quantum harmonic oscillators (Wiley, New York, 1997)
E P Wigner, Phys. Rev. 77, 711 (1950)
Y Ohnuki and S Kamefuchi, Quantum field theory and parastatistics (Springer, New York, 1982)
N Mukunda, E C G Sudarshan, J K Sharma and C L Mehta, J. Math. Phys. 21, 2386 (1980)
J K Sharma, C L Mehta, N Mukunda and E C G Sudarshan, J. Math. Phys. 22, 78 (1981)
E I Jafarov, S Lievens and J Van der Jeugt, J. Phys. A: Math. Theor. 41, 235301 (2008)
R Koekoek, P A Lesky and R F Swarttouw, Hypergeometric orthogonal polynomials and their q-analogues (Springer, Berlin, 2010)
D J BenDaniel and C B Duke, Phys. Rev. 152, 683 (1966)
T Gora and F Williams, Phys. Rev. 177, 1179 (1969)
Q-G Zhu and H Kroemer, Phys. Rev. B 27, 3519 (1983)
O von Roos, Phys. Rev. B 27, 7547 (1983)
O Mustafa and S Habib Mazharimousavi, Int. J. Theor. Phys. 46, 1786 (2007)
O Mustafa, Eur. Phys. J. Plus 134, 228 (2019)
O Mustafa and Z Algadhi, Eur. Phys. J. Plus 135, 559 (2020)
O Mustafa, Eur. Phys. J. Plus 136, 249 (2021)
F D Nobre and M A Rego-Monteiro, Braz. J. Phys. 45, 79 (2015)
S Zare and H Hassanabadi, Adv. High Energy Phys. 2016, 4717012 (2016)
S Zare, M de Montigny and H Hassanabadi, J. Korean Phys. Soc. 70, 122 (2017)
H Hassanabadi and S Zare, Eur. Phys. J. Plus 132, 49 (2017)
H Hassanabadi and S Zare, Mod. Phys. Lett. A 32, 1750085 (2017)
N Jamshir, B Lari and H Hassanabadi, Physica A 565, 125616 (2021)
V Chithiika Ruby, M Senthilvelan and M Lakshmanan, J. Phys. A: Math. Theor. 45, 382002 (2012)
A Abdellaoui and F Benamira, Phys. Scr. 94, 015201 (2019)
A F Nikiforov and V B Uvarov, Special functions of mathematical physics: A unified introduction with applications (Birkhäuser, Basel, Switzerland, 1988)
A P Prudnikov, Yu A Brychkov and O I Marichev, Integrals and series – v.2: Special functions (Gordon and Breach, Amsterdam, The Netherlands, 1992)
Acknowledgements
E I Jafarov acknowledges that this work was supported by the Science Development Foundation under the President of the Republic of Azerbaijan - Grant No. EIF-KETPL-2-2015-1(25)-56/01/1. J Van der Jeugt was supported by the EOS Research Project 30889451.
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Jafarov, E.I., Van der Jeugt, J. Exact solution of the semiconfined harmonic oscillator model with a position-dependent effective mass in an external homogeneous field. Pramana - J Phys 96, 35 (2022). https://doi.org/10.1007/s12043-021-02279-7
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DOI: https://doi.org/10.1007/s12043-021-02279-7