Position-dependent mass momentum operator and minimal coupling: point canonical transformation and isospectrality

Mustafa, Omar; Algadhi, Zeinab

doi:10.1140/epjp/i2019-12588-y

Cited by 60 publications

(93 citation statements)

References 55 publications

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“…wherep = −i∂ x is the regular textbook constant mass momentum operator used in (69) and (70). Finally, the PDM quantum supersymmetric approach with the asymptotic geometrical classical oscillator correspondence by Cruz et al [21], the factorization approach by Mustafa and Mazharimousavi [27], the construction of the PDM-momentum operator approach by Mustafa and Algadhi [10], and the current PDM creation and annihilation oscillator operators approach, all confirm and emphasize that the PDM-Hamiltonian H 1 of (29) is the only surviving one out of the von Roos PDM Hamiltonians. However, the quantization approach of the PDM Noether momentum by Cariñena et al [34], and our analysis and discussions in the current methodical proposal suggest thatĤ 2 of (68) is not only correlated withĤ 1 but also more simplistic user-friendly thanĤ 1 that of (63).…”

Section: Discussionmentioning

confidence: 68%

PDM creation and annihilation operators of the harmonic oscillators and the emergence of an alternative PDM-Hamiltonian

Mustafa

2020

Physics Letters A

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The exact solvability and impressive pedagogical implementation of the harmonic oscillator's creation and annihilation operators make it a problem of great physical relevance and the most fundamental one in quantum mechanics. So would be the position-dependent mass (PDM) oscillator for the PDM quantum mechanics. We, hereby, construct the PDM creation and annihilation operators for the PDM oscillator via two different approaches. First, via von Roos PDM Hamiltonian and show that the commutation relation between the PDM creationÂ + and annihilationÂ operators, [Â,Â + ] = 1 ⇔ÂÂ + − 1/2 =Â +Â + 1/2, not only offers a unique PDM-Hamiltonian H1 but also suggests a PDM-deformation in the coordinate system. Next, we use a PDM point canonical transformation of the textbook constant mass harmonic oscillator analog and obtain yet another set of PDM creationB + and annihilationB operators, hence an "apparently new" PDM-HamiltonianĤ2 is obtained. The "new" PDM-HamiltonianĤ2 turned out to be not only correlated withĤ1 but also represents an alternative and most simplistic user-friendly PDM-Hamiltonian, H = p/ 2m (x) 2 + V (x) ;p = −i ∂x, that has never been reported before.

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Section: Discussionmentioning

confidence: 68%

PDM creation and annihilation operators of the harmonic oscillators and the emergence of an alternative PDM-Hamiltonian

Mustafa

2020

Physics Letters A

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“…− → Q . − → E ) yields only a constant shift in the energy levels given in (32) and (42) creating a new set of energies given in (59) and (63).…”

Section: A the Influence Of A Coulomb-type Electric Field On The Lanmentioning

confidence: 99%

Landau quantization for an electric quadrupole moment of position-dependent mass quantum particles interacting with electromagnetic fields

Algadhi

Mustafa

2020

Annals of Physics

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Analogous to Landau quantization related to a neutral particle possessing an electric quadrupole moment, we generalize such a Landau quantization to include position-dependent mass (PDM) neutral particles. Using cylindrical coordinates, the exact solvability of PDM neutral particles with an electric quadrupole moment moving in electromagnetic fields is reported. The interaction between the electric quadrupole moment of a PDM neutral particle and a magnetic field in the absence of an electric field is analyzed for two different radial cylindrical PDM settings. Next, two particular cases of radial electric fields ( − → E = λ ρ ρ and − → E = λρ 2 ρ) are considered to investigate their influence on the Landau quantization (of this system using the same models of PDM settings). The exact eigenvalues and eigenfunctions for each case are analytically obtained.

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“…where − → A ( − → r ) is the vector potential, eϕ ( − → r ) is a scalar potential and V ( − → r ) is any other potential energy than the electricomagnetic one. In a subsequent work, moreover, Mustafa and Algadhi [11] have constructed and defined the PDM-momentum operator as…”

Section: Introductionmentioning

confidence: 99%

PDM-charged particles in PD-magnetic plus Aharonov–Bohm flux fields: Unconfined “almost-quasi-free” and confined in a Yukawa plus Kratzer exact solvability

Mustafa¹,

Algadhi²

2020

Chinese Journal of Physics

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Using azimuthally symmetrized cylindrical coordinates, we consider some positiondependent mass (PDM) charged particles moving in position-dependent (PD) magnetic and Aharonov-Bohm flux fields. We focus our attention on PDM-charged particles with m ( − → r ) = g (ρ) = η f (ρ) exp (−δρ) (i.e., the PDM is only radially dependent) moving in an inverse power-law-type radial PD-magnetic fieldsUnder such settings, we consider two almost-quasi-free PDM-charged particles (i.e., no interaction potential, V ( − → r ) = 0) endowed with g (ρ) = η/ρ and g (ρ) = η/ρ 2 . Both yield exactly solvable Schrödinger equations of Coulombic nature but with different spectroscopic structures. Moreover, we consider a Yukawa-type PDM-charged particle with g (ρ) = η exp (−δρ) /ρ moving not only in the vicinity of the PD-magnetic and Aharonov-Bohm flux fields but also in the vicinity of a Yukawa plus a Kratzer type potential force field V (ρ) = −V• exp (−δρ) /ρ−V 1 /ρ+V 2 /ρ 2 . For this particular case, we use the Nikiforov-Uvarov (NU) method to come out with exact analytical eigenvalues and eigenfunctions. Which, in turn, recover those of the almost-quasi-free PDM-charged particle with g (ρ) = η/ρ for V• = V 1 = V 2 = 0 = δ.

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Position-dependent mass momentum operator and minimal coupling: point canonical transformation and isospectrality

Cited by 60 publications

References 55 publications

PDM creation and annihilation operators of the harmonic oscillators and the emergence of an alternative PDM-Hamiltonian

PDM creation and annihilation operators of the harmonic oscillators and the emergence of an alternative PDM-Hamiltonian

Landau quantization for an electric quadrupole moment of position-dependent mass quantum particles interacting with electromagnetic fields

PDM-charged particles in PD-magnetic plus Aharonov–Bohm flux fields: Unconfined “almost-quasi-free” and confined in a Yukawa plus Kratzer exact solvability

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