Table of contents

The spectrum of an electron in a dielectric junction is analysed in terms of one-dimensional box-confinement with width 2a and a potential due to images in the two parallel planes. It tends to the spectrum of a particle in a box for a→0, and to the Coulombic spectrum with parity degeneracy for a→∞. Based on some general properties, simple expressions are obtained for the energies of all the states. Model wavefunctions are developed for the first four states which provide a physical insight into their structure.

We demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schrödinger equations governing the nonlinear evolution of the envelopes probe fields in the four-mixing scheme. Four types of solutions are given explicitly, namely new bright–bright, new dark–dark, new bright–dark and new dark–bright solitons.

In this paper, dependent and independent variable transformations are introduced to solve the sine–Gordon (SG) equation by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different kinds of solutions can be obtained for the (SG) equation, including breather solutions and breather lattice solutions.

A striking correlation has been found to exist between the ionic charge and dielectric constants of A^IB^IIIC₂^VI and A^IIB^IVC₂^V chalcopyrite semiconductors. The dielectric constants of these compounds exhibit a linear relationship when plotted on a log–log scale against the nearest neighbour distance d (Å), but fall on different straight lines according to the product of ionic charges of the compounds. A fairly good agreement has been found between the observed and calculated values of the dielectric constants for A^IB^IIIC₂^VI and A^IIB^IVC₂^V semiconductors.

A quantum secure direct communication network scheme is proposed with quantum superdense coding and decoy photons. The servers on a passive optical network prepare and measure the quantum signal, i.e. a sequence of the d-dimensional Bell states. After confirming the security of the photons received from the receiver, the sender codes his secret message on them directly. For preventing a dishonest server from eavesdropping, some decoy photons prepared by measuring one photon in the Bell states are used to replace some original photons. One of the users on the network can communicate to any other one. This scheme has the advantage of high capacity, and it is more convenient than others as only a sequence of photons is transmitted in quantum line.

Chemical effects on the K_i/K_j (i=α₂, β, β₁, β₂; j=α, α₁, β₁), L_i/L_α (i=ℓ, β, γ) and L_i/K_j (i=l,α, β, γ; j=α₁, α₂) x-ray intensity ratios for  (Hf) compounds were investigated. The samples were excited by 123.6 keV γ-rays from a ⁵⁷Co annular radioactive source. K and L x-rays emitted by samples were counted by an Ultra-LEGe detector with a resolution of 150 eV at 5.9 keV. We observed a chemical effect on the L_i/L_a and L_i/K_j x-ray intensity ratios for Hf compounds. However, for the K_i/K_j intensity ratios, dependence on the chemical state of Hf compounds is almost negligible. The experimental values have been compared with the theoretically calculated values of pure Hf.

A scheme of a three-level laser in the presence of usual transmission losses is presented. It is proposed that, if the spontaneous emission between the lasing levels is coupled to a 'squeezed vacuum' reservoir, stability of phase locking can be achieved. The phase diffusion coefficient decreases below the Schawlow–Townes limit and vanishes for larger squeezing.

The Stark broadening of hydrogen radio recombination lines (RRLs), observed from galactic H II regions, is controlled by inelastic collisions with charged particles. There is a dramatic discrepancy—up to several hundred percent—between cross-sections of inelastic electronic collisions (causing the radiative transitions between the Rydberg levels) calculated by various authors. This dramatic discrepancy in cross-sections leads to a significant discrepancy in spectral line widths of RRLs. In this paper, we address two problems: (i) whose results for the cross-sections of the radiative transitions between the Rydberg levels are the most reliable and should be recommended to astrophysicists-observers for their analysis of the measured profiles of RRLs? (ii) How can one allow for all major processes relevant to the Stark broadening of RRLs (transitions between discrete levels, ionization, charge exchange) within a single/unified theoretical approach? For this purpose, we employed calculations in frames of the classical trajectory Monte Carlo approach. We obtained the results for a broad range of velocities of the charged particles (both electrons and protons), including the region most difficult for the analytical description, where the velocities of both the incident particle and the atomic electron have the same order of magnitude. By benchmarking analytical and semi-empirical results of other authors to our calculations (which are non-perturbative and do not use the dipole approximation), we have found which one is the most accurate and should be recommended to astrophysicists-observers for their analysis of the measured profiles of RRLs.

We study the Casimir pressure for a dielectric–diamagnetic cylinder subject to light velocity conservation and with a dispersion law analogous to Sellmeir's rule. Similarities to and differences from the spherical case are pointed out.

In this paper, we have found a series solution of three-dimensional (3D) Einstein equations describing a wormhole for an inhomogeneous distribution of phantom energy. Here, we assume the equation of state is linear but highly anistropic.

Heras (2006 Am. J. Phys. 74 1025–30) has recently claimed that preradiation does not exist according to classical electrodynamics. In the present paper, we show that the theory does indeed predict the existence of preradiation, and that the Schott energy plays an essential role in this connection.

Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in order to obtain a physically correct result. In this paper we will examine this problem and determine why a theory that is supposed to be gauge invariant produces non-gauge invariant results.

For one dimensional systems, we derive from the Dirac spinor equation (DSE) the relativistic quantum stationary Hamilton–Jacobi equation (RQSHJES) for particles of spin . We establish that the RQSHJES ±_1/2 is constituted of two equations, each one corresponding to the positive and negative energies (particle and antiparticle). The solution of the RQSHJES ±_1/2 is well established. We also investigate the Dirac–Klein–Gordon equation and set its corresponding Hamilton–Jacobi equation.

In this paper, we resolve the three-dimensional quantum stationary Hamilton–Jacobi equation (3D-QSHJE) for a general form of the potential, and discuss the nature of the hidden antisymmetric tensor introduced by Bertoldi et al. We derive the 3D quantum law of motion and plot the 3D quantum trajectories of a free particle (electron).

We present very accurate values for the bound state energy eigenvalues by solving the radial Schrödinger equation for the Hulthén potential within the framework of the asymptotic iteration method (AIM) for any ℓ states and for different screening parameters without using any approximations required by other methods. The AIM results are compared with the results of the numerical integration, the generalized pseudospectral, the supersymmetry, the variational and the shifted 1/N expansion methods and they are in very good agreement for different screening parameter, δ, values.

The nonlinear Kelvin–Helmholtz stability of the cylindrical interface between the vapour and liquid phases of a fluid is studied when the phases are enclosed between two cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. The method of multiple time expansion is used for the investigation. The evolution of amplitude is shown be governed by a nonlinear first-order differential equation. The stability criterion is discussed, and the region of stability is displayed graphically.

It is pointed out that oscillons and related solutions of the modified nonlinear Schrödinger equation originally obtained to describe two-dimensional nonlinear surface waves on a plasma are applicable to a variety of problems involving nonlinear oscillations in different media.