PDM-Charged Quantum Particles Moving in Magnetic Fields - Algadhi, Zeinab Saleh Musbah (Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ), 2020)
The classical and quantum mechanical correspondence for constant mass settings is used, along with some nonlocal point transformation (NPT), to find the position-dependent mass (PDM) classical and quantum Hamiltonians. Consequently, the PDM-momentum operator is constructed. The same recipe is followed to identify the form of the PDM-minimal coupling of electromagnetic interactions for the classical and quantum PDM-Hamiltonians. Using azimuthally symmetrized cylindrical coordinates, some PDM-charged particles moving in magnetic (constant or position-dependent (PD)) and Aharonov-Bohm (AB) flux fields along with some interaction potentials are considered. Their separability and solvability under PDM-settings is also reported. Systems of PDM-charged particles moving in three fields: constant magnetic, AB-flux, and pseudoharmonic oscillator potential, or generalized Killingbeck potential fields are solved for different radial cylindrical PDM settings. Spectral signatures of the one-dimensional z-dependent Schr¨odinger part on the overall eigenvalues and eigenfunctions, are reported using two z-dependent potential models (infinite potential well and Morse-type potentials). PDM-charged particles moving in an inverse power-law-type radial PD-magnetic fields are considered. Under such settings, the exact solutions of almost-quasi-free PDM-charged particles (i.e., no interaction potential) endowed with two type of radial cylindrical PDM settings are obtained. Furthermore, a Yukawa-type PDM-charged particle with a specific PDM setting moving in PD-magnetic and AB-flux fields along with Yukawa plus Kratzer type potential force fields is analyzed (using the Nikiforov-Uvarov (NU) method) to come out with exact solutions of the system. Exact or conditionally exact eigenvalues and eigenfunctions are analytically obtained. Keywords: position-dependent mass Hamiltonian, point transformation, PDM - momentum operator, PDM minimal-coupling, cylindrical coordinates, constant magnetic and position-dependent magnetic fields, Aharonov-Bohm flux field, almost-quasi-free PDM-charged particles, pseudo-harmonic osillator and Killingbeck potentials, Yukawa-plus-Kratzer potential, Nikiforov-Uvarov exact solvability.

OZ: Klasik ve Kuantum Mekaniksel tekˆabuliyet ve Yerel Olmayan Nokta D¨on¨us¸ ¨um (YOND) y¨ontemi kullanarak Pozisyon Ba˘gımlı K¨utle (PBK) Hamilton ve momentum operat¨orleri tespit edilmis¸tir. Bu y¨ontemle minimal kuplajlı elektromagnetik etkiles¸meler ic¸in Klasik ve Kuantum PBK-Hamilton fonksiyonları bulunmus¸tur. Eksensel simetrik silindirik koordinatlar kullanarak s¸arjlı partik¨ullerin, sabit (veya pozisyon ba˘gımlı (PB)), magnetik Aharanov–Bohm (AB) akısı ve etkiles¸im potansiyelleri ic¸indeki hareketleri ele alınmıs¸tır. PBK durumunda hareket denklemleri ayrım ve c¸o¨zu¨m ac¸ısından incelenmis¸tir. U¨ c¸ durum ele alınmıs¸tır: Sabit magnetik alan, AB-akısı, sahte harmonik hareket potansiyeli veya genellenmis¸ Killingbeck potansiyel alanlarında radyal silindirik c¸ ¨oz¨umler verilmis¸tir. Tek boyutlu, z–ba˘gımlı Schr¨odinger denkleminin spektral is¸aretlerinden, iki farklı potansiyel (sonsuz kuyu ve Morse–gibi) ic¸in uygun de˘ger ve fonksiyonları elde edilmis¸tir. Burada PBK partik¨ulleri ic¸in ters–¨ustel etkiles¸im alanları durumunda radyal PB-magnetik alan ele alınmıs¸tır. Yaklas¸ık, sahte serbest g¨or¨un¨uml¨u, s¸arjlı PBK durumunda kesin silindirik c¸ ¨oz¨umler verilmis¸tir. ˙Ilˆaveten Yukawa tipi s¸arjlı PBK, PB–magnetik, AB–akılı ve Kratzer tipi potansiyel katkılı alanlar ic¸in Nikiforov–Uvarov (NU) y¨ontemi sayesinde c¸ ¨oz¨umler bulunmus¸tur. Kesin veya s¸artlı uygun de˘ger fonksiyonları elde edilmis¸tir. Anahtar Kelimeler: pozisyon ba˘gımlı k¨utle Hamilton fonksiyonu, momentum operat¨or¨u, minimal kuplaj, silindirik koordinatlar, sabit ve pozisyon ba˘gımlı magnetik alan, Aharanov – Bohm akı alanı, yaklas¸ık serbest pozisyon ba˘gımlı s¸arj partik¨ul, sahte–harmonik titres¸im, Killingbech, Yukawa – Kratzer potansiyelleri, Nikiforov – Uvarov kesin c¸ ¨oz¨uml¨ul¨u˘g¨u.
Doctor of Philosophy in Physics. Institute of Graduate Studies and Research. Thesis (Ph.D.) - Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Physics, 2020. Supervisor: Prof. Dr. Omar Mustafa.
Keywords: Physics; Quantum Physics--Quantum Mechanics--Mass; Particle mechanics; Position-dependent mass Hamiltonian; point transformation; PDM - momentum operator; PDM minimal-coupling; cylindrical coordinates; constant magnetic and position-dependent magnetic fields; Aharonov-Bohm flux field; almost-quasi-free PDM-charged particles; pseudo-harmonic osillator and Killingbeck potentials; Yukawa-plus-Kratzer potential; Nikiforov-Uvarov exact solvability