Omar Mustafa

d-dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass

The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in the Schrodinger equation is described. Illustrative examples including the harmonic oscillator, Coulomb, spiked harmonic, Kratzer, Morse oscillator, Pőschl–Teller and Hulthen potentials are used as reference potentials to obtain exact energy eigenvalues and eigenfunctions for target potentials at different position-dependent mass settings.

Ordering Ambiguity Revisited via Position Dependent Mass Pseudo-Momentum Operators

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, Phys. Lett. A.275 (2000) 25 reliability test and classified as good ordering.

Quantum particles trapped in a position-dependent mass barrier; a d-dimensional recipe

Abstract We consider a free particle, V ( r ) = 0 , with a position-dependent mass m ( r ) = 1 / ( 1 + ς 2 r 2 ) 2 in the d -dimensional Schrodinger equation. The effective potential turns out to be a generalized Poschl–Teller potential that admits exact solution.

Dirac and Klein–Gordon particles in complex Coulombic fields: a similarity transformation

The observation that the existence of the amazing reality and discreteness of the spectrum need not necessarily be attributed to the Hermiticity of the Hamiltonian is re-emphasized in the context of the non-Hermitian Dirac and Klein–Gordon Hamiltonians. Complex Coulombic potentials are considered.

A singular position-dependent mass particle in an infinite potential well

Abstract An unusual singular position-dependent-mass particle in an infinite potential well is considered. The corresponding Hamiltonian is mapped through a point-canonical-transformation and an explicit correspondence between the target Hamiltonian and a Poschl–Teller type reference Hamiltonian is obtained. New ordering ambiguity parametric setting are suggested.

Asymptotic solvability of an imaginary cubic oscillator with spikes

For complex potentials V(x) = −(ix)3 − β2(ix)−2 − 2βδ(ix)1/2 which are symmetric, we show that in β 1 strong coupling regime the low-lying bound states almost coincide with harmonic oscillators whenever the spectrum remains real (this means, at all δ < δcritical(β) ≈ 1).

PT-symmetric pseudo-perturbation recipe: an imaginary cubic oscillator with spikes

The pseudo-perturbative shifted-l expansion technique (PSLET) is shown to be applicable in the non-Hermitian -symmetric context. The construction of bound states for several -symmetric potentials is presented, with special attention paid to V(r) = ir3 − α√ir oscillators.

η-weak-pseudo-Hermiticity generators and exact solvability

Abstract Exact solvability of some non-Hermitian η-weak-pseudo-Hermitian Hamiltonians is explored as a byproduct of η-weak-pseudo-Hermiticity generators. A class of V eff ( x ) = V ( x ) + i W ( x ) potentials is considered, where the imaginary part W ( x ) is used as an η-weak-pseudo-Hermiticity generator to obtain exactly solvable η-weak-pseudo-Hermitian Hamiltonian models.

Non-Hermitian d-dimensional Hamiltonians with position-dependent mass and their η-pseudo-Hermiticity generators

A class of non-Hermitian d-dimensional Hamiltonians with position-dependent mass and their η-pseudo-Hermiticity generators is presented. Illustrative examples are given in 1D, 2D, and 3D for different position-dependent mass settings.

(1+1)-Dirac Particle with Position-Dependent Mass in Complexified Lorentz Scalar Interactions: Effectively \mathcal{PT}-Symmetric

Abstract The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the “quasi-parity” on the Dirac particles’ spectra is also studied. A Dirac particle with PDM and complexified scalar interactions of the form S(z)=S(x−ib) (an inversely linear plus linear, leading to a