dc.contributor.advisor |
Mustafa, Omar |
|
dc.contributor.author |
Abdulrahman, Ibrahim Mustafa |
|
dc.date.accessioned |
2018-04-13T05:54:48Z |
|
dc.date.available |
2018-04-13T05:54:48Z |
|
dc.date.issued |
2016-09 |
|
dc.date.submitted |
2016 |
|
dc.identifier.citation |
Abdulrahman, Ibrahim Mustafa. (2016). Position-dependent Mass Lagrangians: Nonlocal Transformations, Euler-Lagrange Invariance and Exact Solvability. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Physics, Famagusta: North Cyprus. |
en_US |
dc.identifier.uri |
http://hdl.handle.net/11129/3602 |
|
dc.description |
Master of Science in Physics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Physics, 2016. Supervisor: Prof. Dr. Omar Mustafa. |
en_US |
dc.description.abstract |
This thesis reviews some features of the PDM Lagrangians. We reach the mapping of the PDM equation into a unit-mass Lagrangian in the generalized coordinates by the insertion of a nonlocal point transformation. The invariance of the PDM Euler-Lagrange equations under specific conditions is proved. We analyze the dynamical equations obeyed by nonlinear oscillator systems with position-dependent mass. Four classes of such examples with PDM-nonlinear oscillators are specified. They include Mathews-Lakshmanan oscillators, a quadratic nonlinear oscillator, a Morse-type oscillator, and a nonlinear deformation of an isotonic oscillator. Attainment among them the mapping of an isotonic nonlinear oscillator into a PDM deformed isotonic oscillator.
Keywords: classical position-dependent mass, nonlocal point transformation, Euler-Lagrange equations invariance. |
en_US |
dc.description.abstract |
ÖZ :
Bu tez, PDM Lagrangian’ların bazı özelliklerini gözden geçirmektedir. PDM denkleminin genelleştirilmiş koordinatlarda bir birim kütle Lagrangian’ı şeklinde eşlenebilmesine, lokal olmayan nokta dönüşümü ile ulaştık. Belirli koşullar atında PDM Euler-Lagrange denklemlerinin değişmezliği kanıtlanmıştır. Biz dinamik denklemleri analiz ederek konuma bağlı kitlelerle birlikte doğrusal olmayan osilatör sistemleri arasındaki uyumuna baktık. PDM doğrusal olmayan osilatörleri dört sınıfta örnekledik. Bunlar, Mathews-Lakshman osilatörleri, kuadratik doğrusal olmayan osilatör, Morse–tipi osilatör ve doğrusal olmayan deformasyonlu izotonik osilatörü içermektedir. Ayrıca, izotonik doğrusal olmayan osilatörün PDM defrome izotonik osilatörüne eşlenmesine de eriştik.
Anahtar kelimeler: Klasik pozisyon bağımlı kitle, yerel olmayan nokta dönüşümü, Euler-Lagrange denklemlerinin değişmezliği |
en_US |
dc.language.iso |
eng |
en_US |
dc.publisher |
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ) |
en_US |
dc.rights |
info:eu-repo/semantics/openAccess |
en_US |
dc.subject |
Physics Department |
en_US |
dc.subject |
Mass |
en_US |
dc.subject |
classical position - dependent mass |
en_US |
dc.subject |
nonlocal point transformation |
en_US |
dc.subject |
Euler - Lagrange equations invariance |
en_US |
dc.title |
Position-dependent Mass Lagrangians: Nonlocal Transformations, Euler-Lagrange Invariance and Exact Solvability |
en_US |
dc.type |
masterThesis |
en_US |
dc.contributor.department |
Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Physics |
en_US |