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Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System
Joint Authors
Medjber, Salim
Bekkar, Hacene
Menouar, Salah
Choi, Jeong Ryeol
Source
Advances in Mathematical Physics
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-04-19
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
The Schrödinger solutions for a three-dimensional central potential system whose Hamiltonian is composed of a time-dependent harmonic plus an inverse harmonic potential are investigated.
Because of the time-dependence of parameters, we cannot solve the Schrödinger solutions relying only on the conventional method of separation of variables.
To overcome this difficulty, special mathematical methods, which are the invariant operator method, the unitary transformation method, and the Nikiforov-Uvarov method, are used when we derive solutions of the Schrödinger equation for the system.
In particular, the Nikiforov-Uvarov method with an appropriate coordinate transformation enabled us to reduce the eigenvalue equation of the invariant operator, which is a second-order differential equation, to a hypergeometric-type equation that is convenient to treat.
Through this procedure, we derived exact Schrödinger solutions (wave functions) of the system.
It is confirmed that the wave functions are represented in terms of time-dependent radial functions, spherical harmonics, and general time-varying global phases.
Such wave functions are useful for studying various quantum properties of the system.
As an example, the uncertainty relations for position and momentum are derived by taking advantage of the wave functions.
American Psychological Association (APA)
Medjber, Salim& Bekkar, Hacene& Menouar, Salah& Choi, Jeong Ryeol. 2016. Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System. Advances in Mathematical Physics،Vol. 2016, no. 2016, pp.1-6.
https://search.emarefa.net/detail/BIM-1095817
Modern Language Association (MLA)
Medjber, Salim…[et al.]. Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System. Advances in Mathematical Physics No. 2016 (2016), pp.1-6.
https://search.emarefa.net/detail/BIM-1095817
American Medical Association (AMA)
Medjber, Salim& Bekkar, Hacene& Menouar, Salah& Choi, Jeong Ryeol. Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System. Advances in Mathematical Physics. 2016. Vol. 2016, no. 2016, pp.1-6.
https://search.emarefa.net/detail/BIM-1095817
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1095817