Dr Candadi V Sukumar

Abstract:

The connection between the algebra of supersymmetry and the inverse scattering method is used to construct one-dimensional potentials with any specified number of non-degenerate bound states at arbitrary energies. The reflection coefficient of the potential so constructed is related to the reflection coefficient of a reference potential which supports no bound states. It is shown that, by choosing the reference potential to be V=0, it is possible to construct reflectionless potentials with bound states at arbitrary energies. The relationship of this construction based on supersymmetry to other known constructions of reflectionless potentials is established. It is shown that the symmetric reflectionless potential may be expressed as a linear combination of the squares of bound state eigenfunctions with coefficients related to the wavenumbers associated with the bound states.

Abstract:

An expansion scheme is developed for studying corrections to the Alder-Winther theory of Coulomb excitation. The zeroth-order term in the expansion of the excitation cross section is identical to the expression provided by the Alder-Winther theory and there are several kinds of first-order corrections. All of these can be calculated by making simple changes in existing computer programs for the Alder-Winther theory. These corrections can be interpreted as a change in the deflection function for the relative motion and a change in the excitation probabilities due to the deviations of the relative motion from a Rutherford orbit. Some of the terms that describe the change in the excitation probabilities correspond to an energy symmetrisation and others can be interpreted as an angular momentum symmetrisation. Numerical comparisons with results of full quantal coupled-channels calculations are presented. © 1986.

Abstract:

The procedures for finding a new potential (1) by eliminating the ground state of a given potential, (2) by adding a bound state below the ground state of a given potential and (3) by generating the phase equivalent family of a given potential using the supersymmetric pairing of the spectra of the operators A+A- and A-A+ are compared with the application of the Gelfand-Levitan procedure (1955) for the corresponding cases. It is shown how the equivalence of the two procedures may be established. A distinction is made between the modifications of the Jost functions associated with four different types of transformations generated by the concept of a supersymmetric partner to a given Schrodinger equation. It is shown that the Bargmann class of potentials may be generated using suitable combinations of the four types of transformations.

Abstract:

It is shown that every one-dimensional quantum mechanical Hamiltonian H1 can have a partner H2 such that H1 and H2 taken together may be viewed as the components of a supersymmetric Hamiltonian. The term 'supersymmetric Hamiltonian' is taken to mean a Hamiltonian defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this symmetry for the spectra of H1 and H2 are explored. It is shown how the supersymmetric pairing may be utilised to eliminate the ground state of H1, or add a state below the ground state of H1 or maintain the spectrum of H1. It is also explicitly demonstrated that the supersymmetric pairing may be used to generate a class of anharmonic potentials with exactly specified spectra. The complete spectrum of an anharmonic potential so generated consists of all the eigenstates of the simple harmonic oscillator and, in addition, a ground state at a specified energy E which lies arbitrarily below the E=1/2 ground state of the harmonic oscillator.

Abstract:

It is shown that the methods of supersymmetric quantum mechanics can be used to obtain the complete energy spectrum and eigenfunctions of the Dirac equation for an attractive Coulomb potential.