Dr Candadi V Sukumar

Abstract:

A unitary operator UR, which generates a single-mode squeezed state of the simple harmonic oscillator from the vacuum, is discussed. The states generated by UR are of the form psi 0( alpha ) approximately Sigma n alpha n mod n). psi 0( alpha ) are not minimum-uncertainty states but have a small value for the uncertainty product even for large values of the mean number of quanta n; for example, var(q) var(p) approximately 0.74 for n=106.

Abstract:

Three different isospectral Hamiltonians have been generated by eliminating the ground state of a given Hamiltonian using procedures based on the Marchenko equations for left- and right-incident waves and the standard model of supersymmetric quantum mechanics. It is shown that each of the two procedures based on the Marchenko equation is equivalent to the application of two appropriately chosen supersymmetric transformations.

Abstract:

It has been shown previously that a potential V0( chi ) in one dimension which supports no bound states may be used as a reference potential from which, by successive applications of the concept of a supersymmetric partner to a given Hamiltonian, it is possible to find a potential V n( chi ) which supports any specified number n of bound states at any chosen energies Ej, j=1,. . .,n. The reflection coefficient of Vn is related to the reflection coefficient of V0. Various alternative representations of the potentials constructed by this procedure are presented. An illustrative example in which Vn is constructed by using a sech2 chi barrier as the reference potential is discussed.

Abstract:

A systematic procedure for deriving a class of potentials with the underlying symmetry group SU(1,1), starting the commutation relations for the generators of SU(1,1), is presented.

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.