Bulent Gonul

Supersymmetric approach to exactly solvable systems with position-dependent effective masses

We discuss the relationship between exact solvability of the Schrodinger equation with a position-dependent mass and the ordering ambiguity in the Hamiltonian operator within the framework of supersymmetric quantum mechanics. The one-dimensional Schrodinger equation, derived from the general form of the effective mass Hamiltonian, is solved exactly for a system with exponentially changing mass in the presence of a potential with similar behaviour, and the corresponding supersymmetric partner Hamiltonians are related to the effective-mass Hamiltonians proposed in the literature.

Supersymmetric solutions of non-central potentials

Abstract Using the ideas of supersymmetry and shape invariance we show that the eigenvalues of a wide class of non-central potentials can be obtained algebraically in a simple and elegant manner. As an illustration we discuss the generalized coulomb and oscillator systems.

Analytical solutions for the Bohr Hamiltonian with the Woods–Saxon potential

Approximate analytical solutions in closed form are obtained for the five-dimensional Bohr Hamiltonian with the Woods–Saxon potential, taking advantage of the Pekeris approximation and the exactly solvable one-dimensional extended Woods–Saxon potential with a dip near its surface. Comparison with the data for several γ-unstable and prolate deformed nuclei indicates that the potential can describe well the ground state and

Solutions for a generalized Woods?Saxon potential

{\gamma }_{1}

A Note on the Woods-Saxon potential

bands of many prolate deformed nuclei corresponding to a large enough ‘well size’ and diffuseness, while it fails in describing the

SYSTEMATIC SEARCH OF EXACTLY SOLVABLE NON-CENTRAL POTENTIALS

{\beta }_{1}

Exact Treatment of ℓ≠0 States

bands, due to its lack of a hard core, as well as in describing γ-unstable nuclei, because of the small ‘well size’ and diffuseness they exhibit.

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

The s-wave Schrodinger and, to clarify one interesting point encountered in the calculations, Klein–Gordon equations are solved exactly for a single neutron moving in a central Woods–Saxon plus an additional potential that provides the flexibility to construct the surface structure of the related nucleus. The physics behind the solutions and the reliability of the results obtained are discussed carefully with the consideration of other related works in the literature. In addition, the exhaustive analysis of the results reveals the fact that the usual Woods–Saxon potential cannot be solved analytically within the framework of non-relativistic physics, unlike its exactly solvable relativistic consideration.The wave Schrodinger and, to clarify one interesting point encountered in the calculations, Klein-Gordon equations are solved exactly for a single neutron moving in a central Woods-Saxon plus an additional potential that provides a flexibility to construct the surface structure of the related nucleus. The physics behind the solutions and the reliability of the results obtained are discussed carefully with the consideration of other related works in the literature. In addition, the exhaustive analysis of the results reveals the fact that the usual Woods-Saxon potential cannot be solved analytically within the framework of non-relativistic physics, unlike its exactly solvable relativistic consideration.

NEW EXACT TREATMENT OF THE PERTURBED COULOMB INTERACTIONS

The s-wave Schrodinger and, to clarify one interesting point encountered in the calculations, Klein–Gordon equations are solved exactly for a single neutron moving in a central Woods–Saxon plus an additional potential that provides the flexibility to construct the surface structure of the related nucleus. The physics behind the solutions and the reliability of the results obtained are discussed carefully with the consideration of other related works in the literature. In addition, the exhaustive analysis of the results reveals the fact that the usual Woods–Saxon potential cannot be solved analytically within the framework of non-relativistic physics, unlike its exactly solvable relativistic consideration.The wave Schrodinger and, to clarify one interesting point encountered in the calculations, Klein-Gordon equations are solved exactly for a single neutron moving in a central Woods-Saxon plus an additional potential that provides a flexibility to construct the surface structure of the related nucleus. The physics behind the solutions and the reliability of the results obtained are discussed carefully with the consideration of other related works in the literature. In addition, the exhaustive analysis of the results reveals the fact that the usual Woods-Saxon potential cannot be solved analytically within the framework of non-relativistic physics, unlike its exactly solvable relativistic consideration.

MAPPING OF NON-CENTRAL POTENTIALS UNDER POINT CANONICAL TRANSFORMATIONS

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.