Mehmet Kocak

SYSTEMATIC SEARCH OF EXACTLY SOLVABLE NON-CENTRAL POTENTIALS

Recently developed supersymmetric perturbation theory has been successfully employed to make a complete mathematical analysis of the reason behind exact solvability of some non-central potentials. This investigation clarifies once more the effectiveness of the present formalism.

Remarks on Exact Solvability of Quantum Systems with Spatially Varying Effective Mass

Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported in the literature and clarifies the relation between physically acceptable effective mass Hamiltonians.Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported in the literature and clarifies the relation between physically acceptable effective mass Hamiltonians.

MAPPING OF NON-CENTRAL POTENTIALS UNDER POINT CANONICAL TRANSFORMATIONS

Motivated by the observation that all known exactly solvable shape invariant central potentials are inter-related via point canonical transformations, we develop an algebraic framework to show that a similar mapping procedure also exists between a class of non-central potentials. As an illustrative example, we discuss the inter-relation between the generalized Coulomb and oscillator systems.

Supersymmetry and the relationship between a class of singular potentials in arbitrary dimensions

The eigenvalues of the potentials V1(r) = A1/r + A2/r2 + A3/r3 + A4/r4 and V2(r) = B1r2 + B2/r2 + B3/r4 + B4/r6 and of the special cases of these potentials such as Kratzer and Goldman-Krivchenkov potentials, are obtained in N-dimensional space. The explicit dependence of these potentials in higher-dimensional space is discussed, which has not been previously covered.

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

With the consideration of spherical symmetry for the potential and mass function, one-dimensional solutions of nonrelativistic Schrodinger equations with spatially varying effective mass are successfully extended to arbitrary dimensions within the frame of recently developed elegant nonperturbative technique, where the BenDaniel-Duke effective Hamiltonian in one dimension is assumed like the unperturbed piece, leading to well-known solutions, whereas the modification term due to possible use of other effective Hamiltonians in one dimension and, together with the corrections coming from the treatments in higher dimensions, are considered as an additional term like the perturbation. Application of the model and its generalization for the completeness are discussed.

A Search on Dirac Equation

The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schrodinger-like one. Earlier results are discussed in a unified framework, and some solutions of a large class of potentials are given.

Bound State Solutions of Klein–Gordon Equation with the Kratzer Potential

The relativistic problem of spinless particle subject to a Kratzer potential is analysed. Bound state solutions for s-waves are found by separating the Klein–Gordon equation into two parts. Unlike the similar works in the literature, the separation make it possible to see explicitly the relativistic contributions, if any, to the solution in the non-relativistic limit.

Unified treatment of screening Coulomb and anharmonic oscillator potentials in arbitrary dimensions

A mapping is obtained relating radial screened Coulomb systems with low screening parameters to radial anharmonic oscillators in N-dimensional space. Using the formalism of supersymmetric quantum mechanics, it is shown that exact solutions of these potentials exist when the parameters satisfy certain constraints.

AN APPROACH TO POTENTIAL SCATTERING

Recently developed time-independent bound-state perturbation theory is extended to treat the scattering domain. The changes in the partial wave phase shifts are derived explicitly and the results are compared with those of other methods.