|
| Titre : |
Airy function solution for inverted oscillator |
| Type de document : |
texte imprimé |
| Auteurs : |
Halima Tobbal, ; Mustapha Maamache, Directeur de thèse |
| Editeur : |
Setif:UFA |
| Année de publication : |
2016 |
| Importance : |
1 vol (36 f.) |
| Catégories : |
Thèses & Mémoires:Physique
|
| Mots-clés : |
Physique Théorique |
| Résumé : |
Introduction
Today, quantum mechanics is a very signiÂ…cant part to understand several physical phe-
nomena. Generally, a quantum system is described by a few vector spaces and linear operators
acting on these spaces. Vector spaces and their operators represent the states and observables
of the quantum system respectively. The dynamics of a quantum system is determined by an
operator called Hamiltonian H(t); veri…ed a dynamical di¤erential equation called Schrödinger
equation. This equation describes the evolution of state which describes physical system, and
gives energy levels. In many practical situations, the physical parameters that appear in the
expression of the Hamiltonian are determined by time-dependent parameters [1, 2, 3]. The
study of time-dependent Hamiltonian is very important in modeling real physical systems. In
the recent years an extensive e¤ort has been devoted to solving time-dependent quantum sys-
tems, the most interesting aspects of a quantum system with a time-dependent Hamiltonian
is the geometric phase [4], and the evolution of eigenstates for an invariant operator I(t)[5].
in this work we stady the theory of invariant for inverted oscillator, using a linear invariant.
The work done by M.Maamache and Y.Bouguerra and J. R. Choi [6], sincerely, wherein
the gaussian wave-packet solution of inverted oscillator has been determined, and which can be
writeen as a displaced ground state by a displacement operator, the latter allows to construct
coherent states. The main of our work is to determine an other wave-packet solution in the
form of airy function, for the same system, by changing the weight function. The chapter I
illustrate the theory of invariant, Then we give a general idea about coherent states in the
chapter II. Finally we apply the theory of invariant for inverted oscillator in the chapter III,
which contains our result. |
| Côte titre : |
MAPH/0139
|
| En ligne : |
https://drive.google.com/file/d/1e_xHRbH-Jc9visbfrlfzjHkFcAv9ONDN/view?usp=shari [...] |
| Format de la ressource électronique : |
pdf |
Airy function solution for inverted oscillator [texte imprimé] / Halima Tobbal, ; Mustapha Maamache, Directeur de thèse . - [S.l.] : Setif:UFA, 2016 . - 1 vol (36 f.).
| Catégories : |
Thèses & Mémoires:Physique
|
| Mots-clés : |
Physique Théorique |
| Résumé : |
Introduction
Today, quantum mechanics is a very signiÂ…cant part to understand several physical phe-
nomena. Generally, a quantum system is described by a few vector spaces and linear operators
acting on these spaces. Vector spaces and their operators represent the states and observables
of the quantum system respectively. The dynamics of a quantum system is determined by an
operator called Hamiltonian H(t); veri…ed a dynamical di¤erential equation called Schrödinger
equation. This equation describes the evolution of state which describes physical system, and
gives energy levels. In many practical situations, the physical parameters that appear in the
expression of the Hamiltonian are determined by time-dependent parameters [1, 2, 3]. The
study of time-dependent Hamiltonian is very important in modeling real physical systems. In
the recent years an extensive e¤ort has been devoted to solving time-dependent quantum sys-
tems, the most interesting aspects of a quantum system with a time-dependent Hamiltonian
is the geometric phase [4], and the evolution of eigenstates for an invariant operator I(t)[5].
in this work we stady the theory of invariant for inverted oscillator, using a linear invariant.
The work done by M.Maamache and Y.Bouguerra and J. R. Choi [6], sincerely, wherein
the gaussian wave-packet solution of inverted oscillator has been determined, and which can be
writeen as a displaced ground state by a displacement operator, the latter allows to construct
coherent states. The main of our work is to determine an other wave-packet solution in the
form of airy function, for the same system, by changing the weight function. The chapter I
illustrate the theory of invariant, Then we give a general idea about coherent states in the
chapter II. Finally we apply the theory of invariant for inverted oscillator in the chapter III,
which contains our result. |
| Côte titre : |
MAPH/0139
|
| En ligne : |
https://drive.google.com/file/d/1e_xHRbH-Jc9visbfrlfzjHkFcAv9ONDN/view?usp=shari [...] |
| Format de la ressource électronique : |
pdf |
|
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