Comment on ‘Two-dimensional position-dependent massive particles in the presence of magnetic fields’

Abstract

Using the well known position-dependent mass (PDM) von Roos Hamiltonian, Dutra and Oliveira (2009 J. Phys. A: Math. Theor. 42 025304) have studied the problem of twodimensional PDM particles in the presence of magnetic fields. They have reported exact solutions for the wavefunctions and energies. In the first part of their study "PDM-Shrödinger equation in two-dimensional Cartesian coordinates", they have used the so called Zhu and Kroemer's ordering α = −1/2 = γ and β = 0 [5]. While their treatment for this part is correct beyond doubt, their treatment of second part "PDM in a magnetic field" is improper . We address these improper treatments and report the correct presentation for minimal coupling under PDM settings.

Confined Klein–Gordon oscillator from a (2+1)-dimensional Gürses to a Gürses or a pseudo-Gürses space-time backgrounds: Invariance and isospectrality

“…Next, we have considered (in Sect. 3) the confined KGoscillator in a general deformation of the (2+1)-dimensional Gürses space-time background (28). Hereby, we have shown that the resulting confined and deformed KG-oscillator is invariant and isospectral with of the confined KG-oscillator (15) in the (2+1)-dimensional Gürses space-time background (1).…”

“…On the other hand, the introduction of Mathews-Lakshmanan oscillator [25] has activated intensive research studies on "effective" position-dependent mass (PDM in short), both in classical and quantum mechanics [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. PDM is a metaphoric manifestation of the coordinate deformation/transformation [29][30][31].…”

Confined Klein-Gordon oscillators in a spacetime and a pseudo-spacetime with a space-like dislocation: PDM KG-oscillators, isospectrality and invariance

“…It has been studied in the Gödel and Gödel-type spacetime background (e.g., [12][13][14][15][16][17][18][19]), in cosmic string spacetime and Kaluza-Klein theory backgrounds (e.g., [19][20][21][22][23]), in Som-Raychaudhuri [24], in the (2+1)-dimensional Gürses spacetime backgrounds (e.g., [25][26][27][28][29]). The concept of position-dependent effective mass (PDM in short) settings of Mathews-Lakshmanan oscillator [30], on the other hand, has sparked research interest on PDM in both classical and quantum mechanics [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. Such a PDM concept is, in fact, a metaphoric manifestation of coordinate deformation/transformation [34][35][36]39].…”

PDM Damped-Driven Oscillators: Exact Solvability, Classical States Crossings, and Self-Crossings

“…This would keep the longstanding gain-loss balance correlation between the kinetic and potential energies of the system and, consequently, the total energy remains an integral of motion (i.e., the standard structure the textbook Lagrangians/Hamiltonians for conservative systems of course). Such a transformation/deformation recipe would in effect introduce the so called position-dependent effective mass concept (or PDM in short) into classical and quantum mechanics (c.f., e.g., sample of references [3][4][5][6][7][8][9][10][11][12][13][14][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] ). It is, therefore, interesting to study and investigate PDM settings on such DDOs.…”