I. H. Duru

Solution of the path integral for the H-atom

Abstract The Greens function of the H-atom is calculated by a simple reduction of Feynmans path integral to gaussian form.

On the path integral for the potential V = ar−2 + br2

Abstract A simple, alternative path integral formulation for the potential V = ar −2 + br 2 , r ⩾ 0, is presented. This is achieved by mapping the problem to a two-dimensional oscillator and using the method of image paths.

Decay rate for supercurrent in thin wire

We present a new evaluation of the fluctuations triggering the decay of supercurrents. Contrary to the existing treatment available in the literature, our result emerges in a simple and closed form. This is due to the fact that, in a polar decomposition δ = ϱ eiγ of the order parameter, we sum over all azimuthal paths explicitly, thereby arriving at a fluctuation determinant for the ϱ variable alone which can be evaluated exactly.

Quantum treatment of a class of time-dependent potentials

The time-dependent potential V(x-f(t)) is studied by path integrals. It is shown that the problem can be mapped into the static form of the potential plus a linear term with a time-dependent coefficient. After the presentation of the general formulation, some exactly solvable examples are discussed. A perturbative treatment is also suggested.

Introduction of internal coordinates into the infinite-component Majorana equation

Given an infinite-component wave equation describing the global quantum numbers of a system one can introduce various internal dynamical coordinates such that ‘constituents’ will appear to move in an oscillator or in a Kepler potential, or, in principle, in other potentials. This is explicitly shown for the Majorana equation. The space-like solutions of the Majorana equations correspond to the scattering state-solutions in terms of the constituent ‘particles’. Light-like solutions and a generalized second-order Majorana equation are also treated in a similar way. Relation to Dirac’s new wave equation without negative energy solutions is discussed.

Casimir energy for a wedge with three surfaces and for a pyramidal cavity

Casimir energy calculations for the conformally coupled massless scalar field for a wedge defined by three intersecting planes and for a pyramid with four triangular surfaces are presented. The group generated by reflections are employed in the formulation of the required Green functions and the wave functions.

Unitary representations of the two-dimensional Euclidean group in the Heisenberg algebra

E(2) is studied as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the unitary irreducible representations of the group are realized is explicitly constructed. The addition theorem for the Kummer functions is derived.

On the path integrations for the Wood-Saxon and related potentials

Abstract It is demonstrated that the radial path integral for the Wood-Saxon potential for s-waves can be solved by using the path integration over the SU (2) manifold. The wavefunctions and the energy spectrum are obtained. It is shown that the path integrals for the Rosen-Morse and the Hulthen potentials are also solvable in a similar way.

slq(2) realizations for Kepler and oscillator potentials and q-canonical transformations

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Kepler and oscillator potentials are q-deformed. The q-canonical transformation connecting two realizations is given and a general definition for the q-canonical transformation is deduced. A q-Schrodinger equation for a Kepler-like potential is obtained from the q-oscillator Schrodinger equation. The energy spectrum and the ground-state wavefunction are calculated.

Casimir energy in a conical wedge and a conical cavity

Casimir energies for a massless scalar field for a conical wedge and a conical cavity are calculated. The group generated by the images is employed in deriving the Green function as well as the wave functions and the energy spectrum.