Dirac oscillators and the relativisticRmatrix

RelativisticRmatrix and continuum shell model

“…This is reflected in the enormous increase in the 90 Zr single particle energies as shown in column three of Table II. This increase shows that, for these coupling constants, the pions are producing repulsion, just as they did in the Hartree-Fock calculations of QHD [5]. Also shown in Fig.…”

“…The second article (II) 5 demonstrated that Dirac oscillator wave functions 6 , 7 provided an excellent and convenient expansion basis. This article also demonstrated that the R matrix formalism allows one to easily orthogonalize scattering solutions to bound state solutions and to treat non-local potentials; and, hence, to calculate exchange terms in relativistic impulse approximation exactly.…”

Effects of spin on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background

“…(3) is that the curved-space gamma matrices are covariantly constant [31][32][33], i.e., ∇ µ γ λ = 0 (see Appendix A). For the specific basis tetrad (8), the connection is found to be…”

“…Because it is a exactly solvable model, several investigations have been developed in the context of this theoretical framework in the last years. The interest in this issue appears in different contexts, such as quantum optics [2][3][4], supersymmetry [5][6][7], nuclear reactions [8], Clifford algebra [9,10] and noncommutative space [11,12]. Recently, the one-dimensional Dirac oscillator has been verified experimentally by J.…”

The DKP oscillator with a linear interaction in the cosmic string space-time

“…Although the Dirac oscillator is normally introduced within the context of many body theory, relativistic quantum mechanics and quantum chromodynamics (in particular as an interquark potential and also as the confining part of the phenomenological Cornell potential). The interest in this issue appears in different contexts such as quantum optics [7][8][9], supersymmetry [5,10,11], nuclear reactions [12], the hadronic spectrum using the two-body Dirac oscillator [13,14] a new representation for its solutions using the Clifford algebra [15,16], noncommutative space [17,18], thermodynamic properties [19] Lie Algebra symmetries [20], supersymmetric (non-relativistic) quantum mechanics [21] the super symmetric path integral formalism [22] the chiral phase transition in presence of a constant magnetic field [8],the relativistic Landau in presence of external magnetic field [23] the Aharonov-Bohm effect [24,25] condensed matter physical phenomena and graphene [26].…”