Shakir M. Nagiyev

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We propose a discretization strategy for systems with axial symmetry. This strategy replaces the continuous position coordinates by a discrete set of sensor points, on which the discrete wave fields transform covariantly with the group of 2 x 2 symplectic matrices. We examine polar arrays of sensors (i.e., numbered by radius and angle) and find the(More)
— The two-dimensional relativistic configurational ~r-space is proposed and the exactly solvable finite-difference model of the harmonic oscillator in this space is constructed. The wave functions of the stationary states and the corresponding energy spectrum are found for the model under consideration. It is shown that, they have correct non-relativistic(More)
The problem of a one-dimensional harmonic oscillator is one of the important paradigms of the theoretical physics. Its solution in the classical approach is unique and simple, leading to the enormous applications in a wide range of the modern physics [1]. This problem in the non-relativistic quantum approach has at least the same importance, and probably(More)
Exactly solvable N -dimensional model of the quantum isotropic singular oscillator in the relativistic configurational ~rN -space is proposed. It is shown that through the simple substitutions the finite-difference equation for the N -dimensional singular oscillator can be reduced to the similar finite-difference equation for the relativistic isotropic(More)
– Exact approach for the factorization of the relativistic linear singular oscillator is proposed. This model is expressed by the finite-difference Schrödinger-like equation. We have found finite-difference raising and lowering operators, which are with the Hamiltonian operator form the close Lie algebra of the SU (1, 1) group. Introduction. – The singular(More)
Meixner oscillators have a ground state and an ‘energy’ spectrum that is equally spaced; they are a two-parameter family of models that satisfy a Hamiltonian equation with a difference operator. Meixner oscillators include as limits and particular cases the Charlier, Kravchuk and Hermite (common quantum-mechanical) harmonic oscillators. By the(More)
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