Related papers: An $su(1,1)$ algebraic approach for the relativist…
We study the radial part of the Dunkl-Coulomb problem in two dimensions and show that this problem possesses the $su(1,1)$ symmetry. We introduce two different realizations for the $su(1,1)$ Lie algebra and use the theory of irreducible…
We study the Dirac equation with Coulomb-type vector and scalar potentials in D + 1 dimensions from an su(1, 1) algebraic approach. The generators of this algebra are constructed by using the Schr\"odinger factorization. The theory of…
We study the Dunkl oscillator in two dimensions by the $su(1,1)$ algebraic method. We apply the Schr\"odinger factorization to the radial Hamiltonian of the Dunkl oscillator to find the $su(1,1)$ Lie algebra generators. The energy spectrum…
We study a relativistic quantum particle in cosmic string spacetime in the presence of a uniform 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…
An exact approach for the factorization of the relativistic linear singular oscillator is proposed. This model is expressed by the finite-difference Schr\"odinger-like equation. We have found finite-difference raising and lowering…
We apply the Schr\"odinger factorization to construct the generators of the dynamical algebra $su(1,1)$ for the radial equation of the generalized MICZ-Kepler problem.
We apply the Schr\"odinger factorization to construct the ladder operators for hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the…
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…
Based on the fact that the Hamiltonians of the Coulomb many-particle systems are always factorized we develop the two different approaches for analytical solution of the Schr\"{o}dinger equation written for arbitrary few- and many-particle…
The bound-state solutions and the su(1,1) description of the $d$-dimensional radial harmonic oscillator, the Morse and the $D$-dimensional radial Coulomb Schr\"odinger equations are reviewed in a unified way using the point canonical…
We mainly explore the linear algebraic structure like SU(2) or SU(1,1) of the shift operators for some one-dimensional exactly solvable potentials in this paper. During such process, a set of method based on original diagonalizing technique…
The bound eigenfunctions and spectrum of a Dirac hydrogen atom are found taking advantage of the $SU(1, 1)$ Lie algebra in which the radial part of the problem can be expressed. For defining the algebra we need to add to the description an…
We present exact solutions of the Dirac equation in static curved space-time using two distinct algebraic approaches. The first method employs $su(1,1)$ algebra operators together with the tilting transformation, enabling the derivation of…
We study the radial part of the MICZ-Kepler problem in an algebraic way by using the $su(1,1)$ Lie algebra. We obtain the energy spectrum and the eigenfunctions of this problem from the $su(1,1)$ theory of unitary representations and the…
We carry out the complete group classification of the class of (1+1)-dimensional linear Schr\"odinger equations with complex-valued potentials. After introducing the notion of uniformly semi-normalized classes of differential equations, we…
During recent years, exact solutions of position-dependent mass Schr\"odinger equations have inspired intense research activities, based on the use of point canonical transformations, Lie algebraic methods or supersymmetric quantum…
We address the classical factorization problem of a one dimensional Schr\"odinger operator $-\partial^2+u-\lambda$, for a stationary potential $u$ of the KdV hierarchy but, in this occasion, a "parameter" $\lambda$. Inspired by the more…
In this thesis quadratic and cubic algebras, which are extensions of SU(1,1) and SU(2) are studied in detail, with particular attention being given to their construction, their finite and infinite dimensional irreducible representations and…
We consider solutions of the 2x2 matrix Hamiltonians of the physical systems within the context of the su(2) and su(1,1) Lie algebra. Our technique is relatively simple when compared with the others and treats those Hamiltonians which can…
The two parameters quantum algebra $SU_{p,k}(2)$ can be obtained from a single parameter algebra $SU_q(2)$. This fact gives some relations between $SU_{p,k}(2)$ quantities and the corresponding ones of the $SU_q(2)$ algebra. In this paper…