Position-dependent mass momentum operator and minimal coupling: point canonical transformation and isospectrality
Department of Physics, Eastern Mediterranean University, G. Magusa, 10, Mersin, North Cyprus, Turkey
* e-mail: firstname.lastname@example.org
Accepted: 18 February 2019
Published online: 27 May 2019
The classical and quantum-mechanical correspondence for constant mass settings is used, along with some point canonical transformation, to find the position-dependent mass (PDM) classical and quantum Hamiltonians. The comparison between the resulting quantum PDM-Hamiltonian and the von Roos PDM-Hamiltonian implied that the ordering ambiguity parameters of von Roos are strictly determined. Eliminating, in effect, the ordering ambiguity associated with the von Roos PDM-Hamiltonian. This, consequently, played a vital role in the construction and identification of the PDM-momentum operator. The same recipe is followed to identify the form of the minimal coupling of electromagnetic interactions for the classical and quantum PDM-Hamiltonians. It turned out that whilst the minimal coupling may very well inherit the usual form in classical mechanics (i.e., , where is the j-th component of the classical PDM-canonical-momentum), it admits a necessarily different and vital form in quantum mechanics (i.e., , where is the j-th component of the quantum PDM-momentum operator). Under our point transformation settings, only one of the two commonly used vector potentials (i.e., ) is found eligible and is considered for our Illustrative examples.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019