P K Bera

Phase-equivalent potentials from supersymmetric quantum mechanics

Using supersymmetry transformations the authors have constructed closed form expressions for the phase-equivalent partners (PEP) of the Morse and Hulthen potentials and discussed some of their characteristic features in terms of a model calculation. The authors have found that (i) there is no Efimov effect for the PEP of the Morse potential and this results from the effect of elimination of the bound state of the parent potential, and (ii) the PEP of the Hulthen potential may have some interesting application in electron-ion scattering.

The Dalgarno - Lewis method as a perturbation theory

The Dalgarno - Lewis summation technique as used in the Rayleigh - Schrodinger perturbation theory is examined. It is shown that this technique forms an independent perturbation theory and can be used to deal with both bound- and continuum-state problems with some added advantage over other such approaches.

Combined variable-phase supersymmetric quantum mechanics

Methods of supersymmetric quantum mechanics (SUSYQM) are used to derive relations between phase functions which occur in the context of the variable-phase approach to potential scattering. It is shown that the phase-equivalent potentials obtained by the application of SUSYQM are not off-shell equivalent. A case study is presented in support of this.

On integral representations of the Coulomb functions

By dealing with a new integral representation for the irregular s‐wave Coulomb function, exact analytical expressions for the corresponding Jost states in momentum space are constructed, and their usefulness in studying the Coulomb half‐shell scattering is demonstrated. A supersymmetry‐inspired ladder‐operator relation is employed to derive higher partial‐wave generalization of the results presented. Some applications of the integral representation for the associated regular solution are also sought.

ISOSPECTRAL INTERACTIONS FOR THREE-BODY PROBLEMS ON THE LINE

The algebraic methods of supersymmetric quantum mechanics are used to construct isospectral Hamiltonians for the three-particle Calogero problem [F. Calogero, J. Math. Phys. 10, 2191 (1969)]. The similarity and points of contrast of the present study with the corresponding two-body problem are discussed. It is found that the family of isospectral interactions is determined essentially by the angular part of the potential in the basic Hamiltonian. A case study is presented to investigate the nature of the individual member in the family.

Optical theorem and Aharonov-Bohm scattering

A rigorous derivation of the optical theorem (OT) from the conservation of probability flux (CPF) is presented for scattering on an arbitrary spherically symmetric potential inN-spatial dimensions (ND). The constructed expression for the OT is found to yield the corresponding well-known results for two- and three-dimensional cases in a rather natural way. The Aharonov-Bohm (AB) effect is considered as a scattering event of an electron by a magnetic field confined in an infinitely long shielded solenoid and a similar derivation is attempted for an appropriate optical theorem. Our current understanding of the scattering theory is found to be inadequate for the purpose. The reason for this is discussed in some detail.

Coulomb correction to elastic alpha - alpha scattering.

The elastic {alpha}-{alpha} scattering is treated within the framework of a generalized phase-function method (GPFM). This generalization consists in absorbing the effect of Coulomb interaction in the comparison functions for developing the phase equation. Based on values of scattering phase shifts computed by the present method, it is concluded that the GPFM provides an uncomplicated approach to rigorous Coulomb correction in the {alpha}-{alpha} scattering.

Phase-function method from the Riccati form of the Schrodinger equation

The compatibility of the phase-function method with the Riccati form of the Schrodinger equation is investigated and the phase and amplitude equations are derived by using the method of variation of parameters.