su(1, 1) algebraic approach of the Dirac equation with Coulomb-type scalar and vector potentials in D+1 dimensions

Salazar-Ramírez, M.; Martínez, D.; Mota, R. D.; Granados, V. D.

doi:10.1209/0295-5075/95/60002

Cited by 10 publications

(17 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result is in full agreement with the energy spectrum in general dimensions reported in references [25,26,31,32]. In the first two works the energy spectrum was obtained in an analytical way by means of confluent hypergeometric functions, while in the last two works the spectrum was obtained algebraically.…”

Section: Su (1 1) Radial Coherent Statessupporting

confidence: 88%

“…For the D +1-dimensional case it was treated by reducing the uncoupled radial second-order equations to those of the confluent hypergeometric functions [25,26]. In recent works, it has been studied the Dirac equation for the three-dimensional Kepler-Coulomb problem [30], and with Coulomb-type scalar and vector potentials in D+1 dimensions from an su(1, 1) algebraic approach [31]. Also, a Johnson-Lippmann operator has been constructed for Coulomb-type scalar and vector potential in general spatial dimensions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

SU(1,1)coherent states for Dirac–Kepler–Coulomb problem inD+1dimensions with

2014

View full text Add to dashboard Cite

We decouple the Dirac's radial equations in D + 1 dimensions with Coulomb-type scalar and vector potentials through appropriate transformations. We study each of these uncoupled second-order equations in an algebraic way by using an su(1, 1) algebra realization. Based on the theory of irreducible representations, we find the energy spectrum and the radial eigenfunctions. We construct the Perelomov coherent states for the Sturmian basis, which is the basis for the unitary irreducible representation of the su(1, 1) Lie algebra. The physical radial coherent states for our problem are obtained by applying the inverse original transformations to the Sturmian coherent states.

show abstract

Section: Su (1 1) Radial Coherent Statessupporting

confidence: 88%

Section: Introductionmentioning

confidence: 99%

SU(1,1)coherent states for Dirac–Kepler–Coulomb problem inD+1dimensions with

2014

View full text Add to dashboard Cite

show abstract

“…In a similar way, in Refs. [49,50] it has been studied the relativistic Kepler-Coulomb problem and the Dirac equation with Coulomb-type scalar and vector potential in D + 1 dimensions from an algebraic approach by using the Schrödinger factorization to construct the su(1, 1) algebra generators.…”

Section: The Schrödinger Factorization Methodsmentioning

confidence: 99%

Algebraic approach and coherent states for a relativistic quantum particle in cosmic string spacetime

Salazar-Ramírez¹,

Ojeda-Guillén²,

Mota³

2016

Annals of Physics

Self Cite

View full text Add to dashboard Cite

a b s t r a c tWe study a relativistic quantum particle in cosmic string spacetime in the presence of a magnetic field and a Coulomb-type scalar potential. It is shown that the radial part of this problem possesses the su(1, 1) symmetry. We obtain the energy spectrum and eigenfunctions of this problem by using two algebraic methods: the Schrödinger factorization and the tilting transformation. Finally, we give the explicit form of the relativistic coherent states for this problem.

show abstract

“…The above equation can be written as the following system of two first-order differential equations [78][79][80][81] …”

Section: A the Dirac Equation In D Dimensionsmentioning

confidence: 99%

Refined comparison theorems for the Dirac equation with spin and pseudo-spin symmetry in d dimensions

Hall

Zorin

2016

Eur. Phys. J. Plus

View full text Add to dashboard Cite

The classic comparison theorem of quantum mechanics states that if two potentials are ordered then the corresponding energy eigenvalues are similarly ordered, that is to say if Va ≤ V b , then Ea ≤ E b . Such theorems have recently been established for relativistic problems even though the discrete spectra are not easily characterized variationally. In this paper we improve on the basic comparison theorem for the Dirac equation with spin and pseudo-spin symmetry in d ≥ 1 dimensions. The graphs of two comparison potentials may now cross each other in a prescribed manner implying that the energy values are still ordered. The refined comparison theorems are valid for the ground state in one dimension and for the bottom of an angular momentum subspace in d > 1 dimensions. For instance in a simplest case in one dimension, the condition Va ≤ V b is replaced by Ua ≤ U b , where Ui(x) = x 0 Vi(t)dt, x ∈ [0, ∞), and i = a or b.

show abstract

su(1, 1) algebraic approach of the Dirac equation with Coulomb-type scalar and vector potentials in D+1 dimensions

Cited by 10 publications

References 46 publications

SU(1,1)coherent states for Dirac–Kepler–Coulomb problem inD+1dimensions with

SU(1,1)coherent states for Dirac–Kepler–Coulomb problem inD+1dimensions with

Algebraic approach and coherent states for a relativistic quantum particle in cosmic string spacetime

Refined comparison theorems for the Dirac equation with spin and pseudo-spin symmetry in d dimensions

Contact Info

Product

Resources

About