K.V. Bhagwat

Feynman propagator for the δ-function potential

Abstract A new derivation of the Feynman propagator for the Dirac δ-function potential is presented.

Path integration of a two-time quadratic action

Path integration of a general two-time quadratic action characterising memory effects is performed within the framework of Feynmans polygonal path approach. Explicit evaluation of the propagator in exact analytical form is further carried out for the specific kernel used by Feynman in the polaron problem.

A harmonic oscillator perturbed by the potential λx2/(1+gx2)

The eigenvalues of the Hamiltonian H=-d2/dx2+x2+ lambda x2/(1+gx2), with lambda and g as parameters, are studied. A simple numerical procedure where the input data are known exactly and the requirements on the computer memory are not stringent is presented. The results agree very well with the available calculations reported earlier.

On a path integral with a topological constraint

We discuss a new method to evaluate a path integral with a topological constraint involving a point singularity in a plane. The path integration is performed explicitly in the universal covering space. Our method is an alternative to an earlier method of Inomata.

Path integration of a quadratic action with a generalized memory

Abstract Path integration of an action representing a harmonic oscillator with a generalized memory is carried out within the framework of Feynmans polygonal approach. The exact propagator obtained is in the form of an exponential integral over a single variable. Closed analytical results are available for special cases of the memory function.

Exact analysis of the critical behaviour in the driven Dicke model of interacting atoms

A system of N identical two-level atoms occupying the same site (the Dicke model) interacting with one another and driven by a coherent field is considered. From the known exact steady-state atomic density operator, expressions for the atomic observables, their fluctuations and correlation functions are constructed. Asymptotic analysis is used to obtain the behaviour of these atomic variables with respect to the parameters of the driving field in the thermodynamic limit N → ∞. It is shown that the interplay between the parameters of the interatomic interactions and the driving field leads to a critical behaviour as N → ∞. The conditions under which the atomic system shows either a first order or a second order phase transition with respect to the field variables are discussed.

A new derivation of the Feynman propagator for the inverse square potential

Abstract A new derivation of the Feynman propagator for a particle moving in an inverse square potential is presented. The method is based on a direct summation of the Feynman-Dyson perturbation series in a closed analytical form.

A lower bound for ground-state energy by Steiner symmetrisation of the potential

It is shown that Steiner symmetrisation of the potential leads to a lowering of the ground-state energy of the Hamiltonian. Some special cases in which Steiner symmetrisation of the potential leads to the lowering of all the bound-state energy levels of the system are presented. A connection between certain exactly solvable potentials via Steiner symmetrisation is also brought out. Counterexamples are given to show that, in general, the lowering of energy eigenvalues on Steiner symmetrisation does not occur for all levels.

Path integral treatment of Coulomb potential by exact summation of a perturbation series

Abstract A path integral treatment of the Coulomb potential based on exact summation of the Feynman-Dyson perturbation series is presented. It is shown that the approach leads to the evaluation of the radial Green function in a closed analytical form.

Exact analysis of the fluorescent Dicke model in the thermodynamic limit

A system of N identical two-level atoms occupying the same site (Dicke model) driven by a coherent field is considered. From the known exact steady state atomic density operator, exact closed form expressions for the atomic observables, their fluctuations and correlation functions are constructed. Asymptotic analysis is used to obtain the behaviour of these atomic variables with respect to the driven field parameters in the thermodynamic limit N → ∞.