Related papers: Position-dependent-mass; Cylindrical coordinates, …
An integrable hierarchies connected with linear stationary Schr\"odinger equation with energy dependent potentials (in general case) are considered. Galilei-like and scaling invariance transformations are constructed. A symmetry method is…
Energy in nuclear matter is, in practice, completely characterized at different densities and asymmetries, when the density dependencies of symmetry energy and of energy of symmetric matter are specified. The density dependence of the…
It is known that multidimensional complex potentials obeying $\mathcal{PT}$-symmetry may possess all real spectra and continuous families of solitons. Recently it was shown that for multi-dimensional systems these features can persist when…
We propose a model of dynamical noncommutative quantum mechanics in which the noncommutative strengths, describing the properties of the commutation relations of the coordinate and momenta, respectively, are arbitrary energy dependent…
In this work, we readdress the Dirac equation in the position-dependent mass (PDM) scenario. Here, one investigates the quantum dynamics of non-Hermitian fermionic particles with effective mass assuming a $(1+1)$-dimension flat spacetime.…
In a recent paper by Jafarov, Nagiyev, Oste and Van der Jeugt (2020 {\sl J.\ Phys.\ A} {\bf 53} 485301), a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent…
An algebraic method of constructing potentials for which the Schroedinger equation with position dependent mass can be solved exactly is presented. A general form of the generators of su(1,1) algebra has been employed with a unified…
Considerations on the complementary time-dependent coordinate transformations emboding Lorentz transformation (LT) show that the relativistic energy-momentum relationship, implicitly the relativistic mass and energy, do not depend on the…
Symmetry energy terms from macroscopic mass formulae are investigated as generalized polarizabilities of nuclear matter. Besides the neutron-proton (n-p) symmetry energy the spin dependent symmetry energies and a scalar one are also…
It is shown that the well-known relativistic correction of quantum Hamiltonian that is present in textbooks appears after quantization of oversimplified relativistic kinetic energy decomposition. Using the proper expression one obtains the…
Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with…
Given a spatially dependent mass we obtain the two-point Green's function for exactly solvable nonrelativistic problems. This is accomplished by mapping the wave equation for these systems into well-known exactly solvable Schrodinger…
For the models of $N$-body identical harmonic oscillators interacting through potentials of homogeneous degree -2, the unitary operator that transforms a system of time-dependent parameters into that of unit spring constant and unit mass of…
The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant…
For Dirac equation, operator-invariants containing explicit time-dependence in parallel to known time-dependent invariants of nonrelativistic Schr\"odinger equation are introduced and discussed. As an example, a free Dirac particle is…
Based on recent results on quasi-exactly solvable Schrodinger equations, we review a new phenomenological potential class lately reported. In the present paper we consider the quantum differential equations resulting from position dependent…
The present paper engages in a particular attempt to acquire exact analytical eigensolutions of the position-dependent effective mass (PDEM) Schr\"odinger equation for a variety of squared style trigonometric potentials. The algebraic…
We solved the one-dimensional position-dependent mass Dirac equation in the presence of the cusp potential and reported the solutions in terms of the Whittaker functions. We have derived the reflection and transmission coefficients by…
The Casimir-Polder interaction energy between a unipolarizable point atom and a unipolarizable dielectric ring has been limited, until now, to the case when the atom is confined on the axis of symmetry of the ring. We find the generalized…
We study complexified Harmonic Oscillator with a position-dependent mass, termed as Complex Exotic Oscillator (CEO). The complexification induces a gauge invariance [19,11]. The role of PT -symmetry is discussed from the perspective of…