# A hybrid approach for quantizing complicated motion of a charged particle in time-varying magnetic field

## Abstract

Quantum characteristics of a charged particle subjected to a singular oscillator potential under an external magnetic field is investigated via SU(1,1) Lie algebraic approach together with the invariant operator and the unitary transformation methods. The system we managed is somewhat complicated since we considered not only the time-variation of the effective mass of the system but also the dependence of the external magnetic field on time in an arbitrary fashion. In this case, the system is a kind of time-dependent Hamiltonian systems which require more delicate treatment when we study it. The complete wave functions are obtained without relying on the methods of perturbation and/or approximation, and the global phases of the system are identified. To promote the understanding of our development, we applied it to a particular case, assuming that the effective mass slowly varies with time under a time-dependent magnetic field.

- Authors:

- Laboratory of Optoelectronics and Compounds (LOC), Department of Physics, Faculty of Science, University of Ferhat Abbas Setif 1, Setif 19000 (Algeria)
- Department of Radiologic Technology, Daegu Health College, Yeongsong 15, Buk-gu, Daegu 702-722 (Korea, Republic of)

- Publication Date:

- OSTI Identifier:
- 22447596

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 353; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHARGED PARTICLES; EFFECTIVE MASS; HAMILTONIANS; LIE GROUPS; MAGNETIC FIELDS; OSCILLATORS; QUANTIZATION; TIME DEPENDENCE; WAVE FUNCTIONS

### Citation Formats

```
Menouar, Salah, and Choi, Jeong Ryeol, E-mail: choiardor@hanmail.net.
```*A hybrid approach for quantizing complicated motion of a charged particle in time-varying magnetic field*. United States: N. p., 2015.
Web. doi:10.1016/J.AOP.2014.11.014.

```
Menouar, Salah, & Choi, Jeong Ryeol, E-mail: choiardor@hanmail.net.
```*A hybrid approach for quantizing complicated motion of a charged particle in time-varying magnetic field*. United States. doi:10.1016/J.AOP.2014.11.014.

```
Menouar, Salah, and Choi, Jeong Ryeol, E-mail: choiardor@hanmail.net. Sun .
"A hybrid approach for quantizing complicated motion of a charged particle in time-varying magnetic field". United States.
doi:10.1016/J.AOP.2014.11.014.
```

```
@article{osti_22447596,
```

title = {A hybrid approach for quantizing complicated motion of a charged particle in time-varying magnetic field},

author = {Menouar, Salah and Choi, Jeong Ryeol, E-mail: choiardor@hanmail.net},

abstractNote = {Quantum characteristics of a charged particle subjected to a singular oscillator potential under an external magnetic field is investigated via SU(1,1) Lie algebraic approach together with the invariant operator and the unitary transformation methods. The system we managed is somewhat complicated since we considered not only the time-variation of the effective mass of the system but also the dependence of the external magnetic field on time in an arbitrary fashion. In this case, the system is a kind of time-dependent Hamiltonian systems which require more delicate treatment when we study it. The complete wave functions are obtained without relying on the methods of perturbation and/or approximation, and the global phases of the system are identified. To promote the understanding of our development, we applied it to a particular case, assuming that the effective mass slowly varies with time under a time-dependent magnetic field.},

doi = {10.1016/J.AOP.2014.11.014},

journal = {Annals of Physics},

number = ,

volume = 353,

place = {United States},

year = {Sun Feb 15 00:00:00 EST 2015},

month = {Sun Feb 15 00:00:00 EST 2015}

}