| Titre : | Study of Certain Atomic Systems in the Context of Generalized Quantum Mechanics |
| Auteurs : | Lakhdar Sek, Auteur ; Mustapha Moumni, Directeur de thèse ; Mokhtar Falek, Directeur de thèse |
| Type de document : | Monographie imprimée |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2023 |
| Format : | 1 vol. (94 p.) / couv. ill. en coul |
| Langues: | Anglais |
| Résumé : |
In this thesis, we conducted an analytical study at the atomic scale of two-dimensional relativistic deformed bosonic and fermionic oscillator equations for charged particles subject to the effect of a uniform magnetic field. In the first stage, we consider the presence of a
minimal uncertainty in momentum caused by the anti-deSitter space model and we use the Nikiforov Uvarov method (NU) to solve the system. The exact energy eigenvalues and the corresponding wave functions are obtained using Jacobi polynomials, and we find that the deformed spectrum remains discrete even for large values of the principal quantum number. In addition, after evaluating the thermal properties, we find that they have been affected by the deformation of the space at high-temperature regime. In the second stage, we solve the same equations in the non-commutative space using a direct method to obtain the energy spectrums and the wave functions, we detect that the study has similar behaviors to the Landau problem in commutative space. Then, the outcomes of the thermal properties show that the systems have been influenced by the NC space. At the last stage, we generalize both deformations in the relativistic equations, and we solve the systems using the NU method hence we obtained the exact energy spectrums and the wave functions by applying the Jacobi polynomials; in the end, we examine the thermal properties which have been influenced by the two deformations |
| Sommaire : |
Dedication . . .. . . . . i
Acknowledgments . ii 0.1 General Introduction . . . . 1 1 The Relativistic Equations 5 1.1 Introduction . . . .. . . . 5 1.2 Klein Gordon equation . . . . . . 5 1.3 Dirac equation .. . . . . 7 1.4 DKP equation . . . . . . . 11 2 Relativistic oscillators in Anti de-Sitter space 14 2.1 Introduction . . . . . . . . . . 14 2.2 Review of the deformed quantum mechanics relation . . 15 2.3 Nikiforov-Uvarov method . . . . . . 16 2.4 Klein Gordon oscillator in a magnetic field . . . . 17 2.5 Dirac oscillator in magnetic field . . . . . . . 24 2.5.1 Special case for graphene . . . . . . . . . . 27 2.6 DKP oscillator in a magnetic field . . . . . . . . 28 2.6.1 Scalar particle case . . . . . . . 29 2.6.2 Vector particle case . . . . 31 2.7 Thermodynamic properties of KG and DKP equations .. 33 2.8 Thermodynamic properties of Dirac equation . . . 38 3 Relativistic oscillators in Non-Commutative Space 45 3.0.1 Introduction.45 3.1 Klein Gordon Oscillator in a magnetic field in NC space .....48 3.2 Dirac Oscillator in a magnetic field in NC space.........52 3.3 DKP oscillator in a magnetic field in NC space....54 3.3.1 Scalar particle case ..........54 3.3.2 vector case .........55 3.4 Thermodynamic Properties of KG and DKP oscillators in NC space...............57 3.5 Thermodynamic Properties of Dirac oscillators in a magnetic field in NC space 62 4 Relativistic oscillators in a magnetic field in AdS and NC spaces 68 4.1 Introduction .68 4.2 KG oscillator in a magnetic field in AdS and NC spaces........ 68 4.3 Dirac Oscillators in a magnetic field in AdS and NC spaces:.......72 4.4 DKP oscillators in a magnetic field in AdS and NC spaces: ...75 4.4.1 Scalar particle case .75 4.4.2 vector case ...76 4.5 Thermodynamic Properties of KG and DKP in AdS and NC spaces...............78 4.6 Thermodynamic Properties of Dirac in AdS and NC spaces............................83 General Conclusion 91 Bibliography 94 |
| En ligne : | http://thesis.univ-biskra.dz/5999/1/Thesis%20Study%20of%20certain%20atomic%20systems%20in%20the%20context%20of%20generalized%20quantum%20mechanics.pdf |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TPHY/125 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
