Ordering ambiguity revisited via position dependent mass pseudo-momentum operators

Abstract

Ordering ambiguity associated with the von Roos position dependent mass (PDM) Hamiltonian is considered. An affine locally scaled first order differential introduced, in Eq.(9), as a PDM-pseudo-momentum operator. Upon intertwining our Hamiltonian, which is the sum of the square of this operator and the potential function, with the von Roos d-dimensional PDM-Hamiltonian, we observed that the so-called von Roos ambiguity parameters are strictly determined, but not necessarily unique. Our new ambiguity parameters' setting is subjected to Dutra's and Almeida's [11] reliability test and classified as good ordering.

10 pages, no figures, revised/expanded, mathematical presentations in section 2 (Especially, the typological Errors in Eqs.(9)-(12))are now corrected. To appear in the Int. J. Theor. Phys

References in corpus (20)

• Supersymmetry and Quantum Mechanics
• Effective Mass of One 4he Atom in Liquid 3he
• Solutions of the nonrelativistic wave equation with position-dependent effective mass
• Deformed algebras, position-dependent effective masses and curved spaces: An exactly solvable Coulomb problem
• Exact solvability of potentials with spatially dependent effective masses
• Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass
• A general scheme for the effective-mass Schrodinger equation and the generation of the associated potentials
• First-order intertwining operators and position-dependent mass Schrodinger equations in d dimensions
• Nonrelativistic Green's function for systems with position-dependent mass
• Kepler problem in Dirac theory for a particle with position-dependent mass
• Scattering in abrupt heterostructures using a position dependent mass Hamiltonian
• Quantum particles trapped in a position-dependent mass barrier; a d-dimensional recipe
• N-fold Supersymmetry in Quantum Systems with Position-dependent Mass
• The Coulomb - harmonic oscillator correspondence in PT-symmetric quantum mechanics
• d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass
• PT symmetric pseudo-perturbation recipe; an imaginary cubic oscillator with spikes
• Non-Hermitian d-dimensional Hamiltonians with position dependent mass and their $\eta$-pseudo-Hermiticity generators
• $\eta$-weak-Pseudo-Hermiticity generators and exact solvability
• Remarks on exact solvability of quantum systems with spatially varying effective mass
• Ordering ambiguity versus representation

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• $\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass
• Quantum oscillator and Kepler-Coulomb problems in curved spaces: deformed shape invariance, point canonical transformations, and rational extensions
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• Massless KG-oscillators in Som-Raychaudhuri cosmic string spacetime in a fine tuned rainbow gravity
• Comment on 'Two-dimensional position-dependent massive particles in the presence of magnetic fields"
• Landau Quantization for an electric quadrupole moment of Position-Dependent Mass Quantum Particles interacting with Electromagnetic fields
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• Exact solution and coherent states of an asymmetric oscillator with position-dependent mass
• Generalized semiconfined harmonic oscillator model with a position-dependent effective mas
• n-dimensional PDM non-linear oscillators: Linearizability and Euler-Lagrange or Newtonian invariance
• Position-dependent mass charged particles in magnetic and Aharonov-Bohm flux fields: separability, exact and conditionally exact solvability
• PDM-charged particles in PD-magnetic plus Aharonov-Bohm flux fields: unconfined "almost-quasi-free" and confined in a Yukawa plus Kratzer exact solvability
• Rational extension and Jacobi-type {\boldmath{$X_m$}} solutions of a quantum nonlinear oscillator
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• Infinite families of position-dependent mass Schrödinger equations with known ground and first excited states
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• Novel exactly solvable Schrödinger equations with a position-dependent mass in multidimensional spaces obtained from duality
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• Modifications in the photoionization cross-section of a quantum dot with position-dependent effective mass
• Dynamics of the Modified Emden and pseudo-Modified Emden Equations: position-dependent mass, invariance and exact solvability
• Impact of the non-canonical approach to the exact solution of the ideal one-dimensional electron gas confined with an anisotropic quantum wire of oscillator-shaped profile