Shifted-l Expansion Technique Research Articles

ON THE IMPLICATIONS OF A DILATON IN GAUGE THEORY

Some recent work on the implications of a dilaton in 4 d gauge theories are revisited. In part I of this paper we see how an effective dilaton coupling to gauge kinetic term provides a simple attractive mechanism to generate confinement. In particular, we put emphasis on the derivation of confining analytical solutions and look into the problem how dilaton degrees of freedom modify Coulom potential and when a confining phase occurs. In part II, we solve the semi-relativistic wave equation, for Dick interquark potential using the Shifted l-expansion technique (SLET) in the heavy quarkonium sector. The results of this phenomenological analysis proves that these effective theories can be relevant to model quark confinement and may shed some light on confinement mechanism.

Reply to Comment On large-N expansion

Fernandez Comment [1] on our pseudo-perturbative shifted-l expansion technique [2,3] is either unfounded or ambiguous.

PT-symmetric pseudo-perturbation recipe: an imaginary cubic oscillator with spikes

The pseudo-perturbation shifted-l expansion technique PSLET is shown applicable in the non-Hermitian PT-symmetric context. The construction of bound states for several PT-symmetric potentials is presented, with special attention paid to V(r) = ir^3-alpha sqrt(ir) oscillators.

THE SEMIRELATIVISTIC EQUATION VIA THE SHIFTED-l EXPANSION TECHNIQUE

The semirelativistic wave equation which appears in the theory of relativistic quark–antiquark bound states, is cast into a constituent second order Schrödinger-like equation with the inclusion of relativistic corrections up to order (v/c)2 in the quarks speeds. The resulting equation is solved via the Shifted-l expansion technique (SLET), which has been recently developed to get eigenvalues and wave functions of relativistic and nonrelativistic wave equations. The Coulomb, Oscillator, and the Coulomb-plus-linear potentials used in [Formula: see text] phenomenology are tested. It is observed that, the energy eigenvalues can be explained well upon the more commonly used nonrelativistic models, when such a dynamical relativistic corrections are introduced. In particular, it provides a remarkable accurate and simple analytic expression for the Coulomb ground-state energy problem, a result which is in the right direction at least to serve as a test of this approach.

2D H-Atom in an Arbitrary Magnetic Field via Pseudoperturbation Expansions Through the Quantum Number l

The pseudoperturbative shifted-l expansion technique is introduced to determine nodeless states of the 2D Schrodinger equation with arbitrary cylindrically symmetric potentials. Exact energy eigenvalues and eigenfunctions for the 2D Coulomb and harmonic oscillator potentials are reproduced. Moreover, exact energy eigenvalues, compared with those obtained by numerical solution (V.M. Villalba and R. Pino, J. Phys.: Condens. Matter 8 (1996) 80671, were obtained for the hybrid of the 20 Coulomli and oscillator potentials.

Relativistic Shifted-l Expansion Technique for Dirac and Klein-Gordon Equations

The shifted-l expansion technique (SLET) is extended to solve for Dirac particle trapped in spherically symmetric scalar and/or 4-vector potentials. A parameter λ = 0,1 is introduced in such a way that one can obtain the Klein-Gordon (KG) bound states from Dirac bound states. The 4-vector Coulomb, the scalar linear, and the equally mixed scalar and 4-vector power-law potentials are used in KG and Dirac equations. Exact numerical results are obtained for the 4-vector Coulomb potential in both KG and Dirac equations. Highly accurate and fast converging results are obtained for the scalar linear and the equally mixed scalar and 4-vector power-law potentials.

Nonrelativistic Shifted-l Expansion Technique for Three- and Two-Dimensional Schrödinger Equation

The shifted-l expansion techniques (SLET) has been developed to get eigenvalues of Schrödinger equation in three (3D) and two dimensions (2D). SLET simply consists of as a perturbation parameter, where is a suitable shift, l is the angular-momentum quantum number for the 3D-case, for the 2D-case, and m is the magnetic quantum number. Unlike the shifted large-N expansion theory (SLNT), SLET seems to be applicable to a wider number of problems of significant interest in physics.