Quasipotential equation for a relativistic harmonic oscillator

Model of a relativistic oscillator in a generalized Schrödinger picture

“…Quasipotential models of a relativistic oscillator were first considered in [3,4,5]. The ρ-representation or the ρn representation (|n| = 1) may also be used in a so-called generalized Schrödinger (GS) picture in which the analogs of the Schrödinger operators of a particle are independent of both the time and the space coordinates t, x in different representations [6].…”

“…The ρ-representation or the ρn representation (|n| = 1) may also be used in a so-called generalized Schrödinger (GS) picture in which the analogs of the Schrödinger operators of a particle are independent of both the time and the space coordinates t, x in different representations [6]. The one-dimensional motion of a free particle in the ρ-representation is described by the equations ih ∂ ∂t ψ(ρ, t, x) = H(ρ)ψ(ρ, t, x), −ih ∂ ∂x ψ(ρ, t, x) = P (ρ)ψ(ρ, t, x), (3) where the Hamilton operator H(ρ) and the momentum operator P (ρ) have the form H(ρ) = mc 2 cosh(− ih mc ∂ ρ ), P (ρ) = mc sinh(− ih mc ∂ ρ ).…”

The relativistic two-dimensional harmonic oscillator

“…The purpose of this paper is to construct the relativistic model of the two-dimensional harmonic oscillator [2]. Our construction is based on the relativistic finite-difference quantum mechanics, developed in [10][11][12][13][14][15][16][17][18][19][20]. Here, the relativistic configuration space is the key conception [14].…”

A relativistic model of the isotropic three-dimensional singular oscillator

“…In the present paper we generalize this model to the three-dimensional case. Our three-dimensional model is formulated in the framework of the finite-difference relativistic quantum mechanics, which was developed in several papers and applied to the solution of a lot of problems in particle physics [6,7], [17]- [28].…”