Quantization of the fractional harmonic oscillator in terms of Riesz fractional derivatives
Other Title(s)
Quantization of the fractional harmonic oscillator in terms of Riesz fractional derivatives
Dissertant
al-Rawashidah, Muhammad Ibrahim
Thesis advisor
Comitee Members
Ghasib, Hammam B.
Mahmud, Sami
al-Jamal, Ahmad Fawwaz
University
Al albayt University
Faculty
Faculty of Sciences
Department
Department of Physics
University Country
Jordan
Degree
Master
Degree Date
2010
English Abstract
Fractional Lagrangians and fractional Hamiltonians for systems containing Riesz fractional derivatives (RFDs) have been formulated.
The Hamilton's equations of motion are derived.
Besides, the Hamilton-Jacobi formulations for these corresponding systems have been developed using the canonical method.
The relevant Hamilton–Jacobi function has been obtained.
An example for the fractional harmonic oscillator is discussed.
The traditional results are recovered for integer-order derivatives.
The path integral quantization of the fractional harmonic oscillator using Riesz-Caputo fractional derivatives (RCFD) has been performed.
A Lagrangian for a damped Harmonic oscillator has been proposed in terms of Riesz’s Fractional derivative, and the corresponding equation of motion has been obtained.
Main Subjects
Topics
No. of Pages
35
Table of Contents
Table of contents.
Abstract.
Chapter One : introduction.
Chapter Two : fractional derivatives.
Chapter Three : fractional Hamilton’s Jacobi .
Chapter Four : path integral quantization.
Chapter Five : a lagrangian formulation for the damped harmonic oscillator.
Chapter Six : conclusion.
References.
American Psychological Association (APA)
al-Rawashidah, Muhammad Ibrahim. (2010). Quantization of the fractional harmonic oscillator in terms of Riesz fractional derivatives. (Master's theses Theses and Dissertations Master). Al albayt University, Jordan
https://search.emarefa.net/detail/BIM-314946
Modern Language Association (MLA)
al-Rawashidah, Muhammad Ibrahim. Quantization of the fractional harmonic oscillator in terms of Riesz fractional derivatives. (Master's theses Theses and Dissertations Master). Al albayt University. (2010).
https://search.emarefa.net/detail/BIM-314946
American Medical Association (AMA)
al-Rawashidah, Muhammad Ibrahim. (2010). Quantization of the fractional harmonic oscillator in terms of Riesz fractional derivatives. (Master's theses Theses and Dissertations Master). Al albayt University, Jordan
https://search.emarefa.net/detail/BIM-314946
Language
English
Data Type
Arab Theses
Record ID
BIM-314946
