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.
