New Exact Treatment of the Perturbed Coulomb Interactions

Abstract

A novel method for the exact solvability of quantum systems is discussed and used to obtain closed analytical expressions in arbitrary dimensions for the exact solutions of the hydrogenic atom in the external potential ΔV(r) = br + cr2, which is based on the recently introduced supersymmetric perturbation theory.

An alternative treatment for Yukawa-type potentials

“…The applications [8] of this novel treatment to different problems in both, bound and continuum regions, have been proven the success of the formalism. With the confidence gained from these applications, and bearing in mind the significance of a reliable algebraic solution for Yukawa-type potentials, that is clearly reported in [6], we demonstrate here how such interaction potentials can be simply treated within the framework of the present formalism.…”

“…We present only those formulae that are necessary for understanding the following calculations; all details and the mathematical foundations can be found in [7,8]. In section 3…”

A New Algebraic Approach to Perturbation Theory

“…Considering such drawbacks of the available treatments and gaining confidence from the success of the recent works [11], this Letter presents an alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics, which yields simple but closed perturbation theory formulae leading to the Riccati equation from which one can actually obtain all the perturbation corrections to both energy level shifts and wavefunctions for all state. These quantities can be calculated to any given accuracy since the generation of successive corrections in the present perturbative expansions only requires the solution of simple algebraic solutions.…”

Explicit solutions for N-dimensional Schrödinger equations with position-dependent mass

“…Gaining confidence from the successful applications [1] of the recently developed simple model [2] in different fields of physics, we have investigated [3] the relation between the solutions of physically acceptable effective mass Hamiltonians proposed in the literature for the treatment of one dimensional problems. Using the spirit of the prescription suggested in [3], we aim here to tackle the more difficult problem of generating exact solutions for position-dependent mass Schrödinger equations (PDMSE) in N−dimension, as the most of the related works in the literature have been devoted to one-dimensional systems except the ones in [4].…”