Interference of Charged Particles in a Vector Potential with Vanishing Magnetic Field

An interference experiment in a magnetic field free region with non vanishing vector potential created by two perpendicularly intersecting planes carrying uniform currents is discussed. The relation of this configuration to the Aharonov-Bohm potential is examined. An experimental set up which is finite in the direction of the electronic motion is studied.Comment: Latex, 7 pages, 2 figures on request, RIBS-PH-97/

Casimir Energy due to a Semi-Infinite Plane Boundary

Following the derivation of the Green function for the massless scalar field satisfying the Dirichlet boundary condition on the Plane (x > 0, y = 0), we calculate the Casimir energy.Comment: 4 pages, Late

Uncertainty Relations and Wave Packets on the Quantum Plane

(2+2)-dimensional quantum mechanical q-phase space which is the semi-direct product of the quantum plane E_q(2)/U(1) and its dual algebra e_q(2)/u(1) is constructed. Commutation and the resulting uncertainty relations are studied. ``Quantum mechanical q-Hamiltonian'' of the motion over the quantum plane is derived and the solution of the Schroedinger equation for the q-semiclassical motion governed by the expectation value of that Hamiltonian is solved.Comment: Latex, 17 page

Path Integration for the Plane Pendulum with Finite Amplitude

Exact path integration for the one dimensional potential $V=b^2\cos 2q$ which describes the finite amplitude pendulum is presented.Comment: Latex, 6 page

Casimir Energy in a Conical Wedge and a Conical Cavity

Casimir energy 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 functions as well as the wave functions and the energy spectrum.Comment: 9 pages, 2 figure

Planscherel Measure on E_q(2)

Following the construction of the invariant integral and the scalar product for the quantum Euclidean group E_q(2), we obtained the full matrix elements of its unitary irreducible representations from SU_q(2) by contraction and then derived the Planscherel measure.Comment: Latex, 17 page

Quantum Analogue of the Neumann Function of Integer Order

q-Neumann function of integer order N_n(x,q) is obtained and some of its properties are given. q-Psi function which is used in deriving N_n(x,q) is also introduced and some of its properties are presented.Comment: latex, 6 page

Integer powers of complex anti-tridiagonal matrices and some complex factorizations

In this paper, we obtain a general expression for the entries of the rth power of a certain n-square complex anti-tridiagonal matrix where if n is odd, r is integer or if n is even, r is natural number. In addition, we get the complex factorizations of Fibonacci polynomials, Fibonacci and Pell numbers

Integer Powers of Certain Complex (2k+1)-diagonal Toeplitz Matrices

In this paper, we obtain a general expression for the entries of the lth (l is integer) powers of even order (2k+1)-diagonal Toeplitz matrices. Additionally, we have the complex factorizations of Fibonacci polynomials

A Simple Path Integration For the Time Dependent Oscillator

Feynman propagator is calculated for the time dependent harmonic oscillator by converting the problem into a free particle motionComment: Latex, 5 page