| Titre : | Quantum Studies of Some Non-Central Potentials |
| Auteurs : | Mebarek Heddar, Auteur ; Mustapha Moumni, 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, 2021 |
| Format : | 1 vol. (212 p.) / couv. ill. en coul / 30 cm |
| Langues: | Anglais |
| Mots-clés: | Schrödinger equation,Non-Central Potentials,de Sitter and anti-de Sitter Space |
| Résumé : |
In this thesis we conducted a quantum study of non-central potentials that can be studied analytically, where we addressed the solvable potentials in the 2D ordinary space where we addressed both the relativistic and non-relativistic states and as a results of the study we concluded the energy spectrum and the wave function of a charged particle circulating in these potentials ,in this case we studied in detail the Kratzer potential plus dipole potential, then the pseudoharmonic oscillator potential plus dipole potential. In the second stage, with the same previous study, we dealt with other potentials that can be solved in the 3D ordinary space, where in this case we studied in detail the ring-shaped potential plus Kratzer potential, then the ring-shaped potential plus the pseudoharmonic oscillator potential. In the final stages, we treated the same potentials with the same dimensions, but in the deformed space (de Sitter and anti-de Sitter) where we noted the influence of the deformation coefficient on the energy spectrum and its effect on the wave function, then we deduced the critical values of the deformation coefficient for the existence of bound states |
| Sommaire : |
List of Figures III List of Tables IX 0.1 General introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 I The Quantum Studies of Some Non-Central Potentials in Ordinary Space 5 1 Studies of Two Dimensional Non-Central Potentials 7 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Non-Relativistic Studies of 2D Non-Central Potentials . . . . . . . . . . . . . 9 1.2.1 2D Schrödinger Equation . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.2 Non-relativistic Energy and Wave Function (Applications ) . . . . . . 13 1.3 Relativistic Studies of 2D Non-Central Potentials . . . . . . . . . . . . . . . 46 1.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1.3.2 Klein-Gordon Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 54 1.3.3 Dirac Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 1.3.4 Solutions of Schrödinger Type Equation . . . . . . . . . . . . . . . . 57 1.3.5 Relativistic Energy and Wave function (Applications) . . . . . . . . . 58 1.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 2 Studies of Three Dimensional Non-Central Potentials 75 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.2 Non-Relativistic Studies of 3D Non-Central Potentials . . . . . . . . . . . . . 82 2.2.1 3D Schrödinger Equation . . . . . . . . . . . . . . . . . . . . . . . . . 82 2.2.2 Non-Relativistic Energy and Wave Function (Applications) . . . . . . 84 2.3 Relativistic Studies of 3D Non-Central Potentials . . . . . . . . . . . . . . . 102 2.3.1 Solutions of Schrödinger Type Equation . . . . . . . . . . . . . . . . 102 2.3.2 Relativistic Energy and Wave Function (Applications) . . . . . . . . 106 2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 II The Quantum Studies of Some Non-Central Potentials in Deformed Space (deSitter Space and Anti deSitter Space ) 113 3 Studies of N-C Potentials in 2D (dS and AdS) Spaces 115 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 3.1.1 Review of the Deformed Quantum Mechanics Relations . . . . . . . . 116 3.2 2D Schrödinger Equation of N-C Potential in (dS and AdS) Spaces . . . . . 117 3.3 Non-Relativistic Solutions of N-C Potentials in 2D Deformed Space . . . . . 119 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 4 Studies of N-C Potentials in 3D (dS and AdS ) Spaces 147 4.1 3D Schrödinger Equation of N-C Potentials in Deformed Space . . . . . . . . 147 4.2 Non-Relativistic Solutions of N-C Potentials in 3D Deformed Space . . . . . 148 4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 General Conclusion 173 Appendix 175 .1 Details of Non-Central Potential in 2D Ordinary Space . . . . . . . . . . . . 175 .2 Details of Non-Cenral Potentials in 3D Ordinary Space . . . . . . . . . . . . 182 Afterword 189 Bibliography 191 |
| En ligne : | http://thesis.univ-biskra.dz/5393/1/%D8%A7%D8%B7%D8%B1%D9%88%D8%AD%D8%A9%20%D8%AF%D9%83%D8%AA%D9%88%D8%B1%D8%A7%D9%87%20%D8%B9%D9%84%D9%88%D9%85%20%D9%87%D8%AF%D8%A7%D8%B1%20%D9%85%D8%A8%D8%A7%D8%B1%D9%83.pdf |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TPHY/107 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
