Completeness of the Coulomb wave functions in quantum mechanics

We give an explicit, direct, and fairly elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses only some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory; therefore it would form useful supplementary reading for a graduate course on quantum mechanics.

Investigation of the effect of nonlocal scale on ultrasonic wave dispersion characteristics of a monolayer graphene

In this article, an ultrasonic wave propagation in graphene sheet is studied using nonlocal elasticity theory incorporating small scale effects. The graphene sheet is modeled as an isotropic plate of one-atom thick. For this model, the nonlocal governing differential equations of motion are derived from the minimization of the total potential energy of the entire system. An ultrasonic type of wave propagation model is also derived for the graphene sheet. The nonlocal scale parameter introduces certain band gap region in in-plane and flexural wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. The explicit expressions for cutoff frequencies and escape frequencies are derived. The escape frequencies are mainly introduced because of the nonlocal elasticity. Obviously these frequencies are function of nonlocal scaling parameter. It has also been obtained that these frequencies are independent of y-directional wavenumber. It means that for any type of nanostructure, the escape frequencies are purely a function of nonlocal scaling parameter only. It is also independent of the geometry of the structure. It has been found that the cutoff frequencies are function of nonlocal scaling parameter (e(0)a) and the y-directional wavenumber (k(y)). For a given nanostructure, nonlocal small scale coefficient can be obtained by matching the results from molecular dynamics (MD) simulations and the nonlocal elasticity calculations. At that value of the nonlocal scale coefficient, the waves will propagate in the nanostructure at that cut-off frequency. In the present paper, different values of e(o)a are used. One can get the exact e(0)a for a given graphene sheet by matching the MD simulation results of graphene with the results presented in this paper. (C) 2010 Elsevier B.V. All rights reserved.

The Alfvén Wave Equation for Magnetospheric Plasmas

It is shown that besides the continuous spectrum which damps away as inverse power of time, the coupled Alfvén wave equation, which gives coupling between a shear Alfvén wave and a surface wave, can also admit a well behaved harmonic solution in the closed form for a set of initial conditions. This solution, though valid for finite time intervals, points out that the Alfvén surface waves can have a band of frequency (instead of a monochromatic frequency for a nonsheared magnetic field) within which the local field line resonance frequency can lie, and thus can excite magnetic pulsations with latitude-dependent frequency. By considering magnetic fields not only varying in magnitude but also in direction, it is shown that the time interval for the validity of the harmonic solution depend upon the angle between the magnetic field directions on either side of the magnetopause. For small values of the angle the time interval can become appreciably large.

Topological defects in crystals: A density-wave theory

A new approach for describing dislocations and other topological defects in crystals, based on the density wave theory of Ramakrishnan and Yussouff is presented. Quantitative calculations are discussed in brief for the order parameter profiles, the atomic configuration and the free energy of a screw dislocation with Burgers vector b = (a/2, a/2,a/2 ) in a bcc solid. Our results for the free energy of the dislocation in a crystal of sizeR, when expressed as (λb 2/4π) ln (αR/|b|) whereλ is the shear elastic constant, yield, for example, the valueα ⋍ 1·85 for sodium at its freezing temperature (371°K). The density distribution in the presence of the dislocation shows that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order parameter theory incorporating thermal effects.

Microscopic expression for frequency and wave vector dependent dielectric constant of a dipolar liquid

A microscopic expression for the frequency and wave vector dependent dielectric constant of a dense dipolar liquid is derived starting from the linear response theory. The new expression properly takes into account the effects of the translational modes in the polarization relaxation. The longitudinal and the transverse components of the dielectric constant show vastly different behavior at the intermediate values of the wave vector k. We find that the microscopic structure of the dense liquid plays an important role at intermediate wave vectors. The continuum model description of the dielectric constant, although appropriate at very small values of wave vector, breaks down completely at the intermediate values of k. Numerical results for the longitudinal and the transverse dielectric constants are obtained by using the direct correlation function from the mean‐spherical approximation for dipolar hard spheres. We show that our results are consistent with all the limiting expressions known for the dielectric function of matter.

Uniformly valid analytical solution to the problem of a decaying shock wave

An explicit representation of an analytical solution to the problem of decay of a plane shock wave of arbitrary strength is proposed. The solution satisfies the basic equations exactly. The approximation lies in the (approximate) satisfaction of two of the Rankine-Hugoniot conditions. The error incurred is shown to be very small even for strong shocks. This solution analyses the interaction of a shock of arbitrary strength with a centred simple wave overtaking it, and describes a complete history of decay with a remarkable accuracy even for strong shocks. For a weak shock, the limiting law of motion obtained from the solution is shown to be in complete agreement with the Friedrichs theory. The propagation law of the non-uniform shock wave is determined, and the equations for shock and particle paths in the (x, t)-plane are obtained. The analytic solution presented here is uniformly valid for the entire flow field behind the decaying shock wave.

Electromagnetic wave propagation at the interface between two polar semiconductors

The interface between two polar semiconductors can support three types of phonon-plasmon-polariton modes propagating in three well-defined frequency windows ??1?[min(?1,?3),?R1], ??2?[max(?2,?4),?R2], and ??3?[min(?2,?4),?R3]. The limiting frequencies ?1,2,3,4 are defined by ?1(?)=0, ?2(?)=0, and ?R1,2,3 by ?1(?)+?2(?)=0, where ?i(?) are dielectric functions of the two media with i=1,2. The dispersion, decay distances, and polarization of the three modes are discussed. The variation of the limiting frequencies with the interface plasma parameter ???p22/?p12 reveals an interesting feature in the dispersion characteristics of these modes. For the interfaces for which the bulk coupled phonon-plasmon frequencies of medium 1 are greater than the LO frequency or are less than the TO frequency of medium 2, there exist two values of ?=?1 and ?2(

Performance study of high operating temperature HgCdTe mid wave infrared detector through numerical modeling

The design of present generation uncooled Hg1-xCdxTe infrared photon detectors relies on complex heterostructures with a basic unit cell of type (n) under bar (+)/pi/(p) under bar (+). We present an analysis of double barrier (n) under bar (+)/pi/(p) under bar (+) mid wave infrared (x = 0.3) HgCdTe detector for near room temperature operation using numerical computations. The present work proposes an accurate and generalized methodology in terms of the device design, material properties, and operation temperature to study the effects of position dependence of carrier concentration, electrostatic potential, and generation-recombination (g-r) rates on detector performance. Position dependent profiles of electrostatic potential, carrier concentration, and g-r rates were simulated numerically. Performance of detector was studied as function of doping concentration of absorber and contact layers, width of both layers and minority carrier lifetime. Responsivity similar to 0.38 A W-1, noise current similar to 6 x 10(-14) A/Hz(1/2) and D* similar to 3.1 x 10(10)cm Hz(1/2) W-1 at 0.1 V reverse bias have been calculated using optimized values of doping concentration, absorber width and carrier lifetime. The suitability of the method has been illustrated by demonstrating the feasibility of achieving the optimum device performance by carefully selecting the device design and other parameters. (C) 2010 American Institute of Physics. doi:10.1063/1.3463379]

Exploring glueball wave functions on the lattice

We calculate the string tension and 0++ and 2++ glueball masses in pure gauge QCD using an improved lattice action. We compare various smearing methods, and find that the best glueball signal is obtained using smeared Wilson loops of a size of about 0.5 fm. Our results for mass ratios m0++/√σ=3.5(3) and m2++/m0++=1.6(2) are consistent with those computed with the simple plaquette action.

Structure and representation of correlation functions and the density matrix for a statistical wave field in optics

A systematic structure analysis of the correlation functions of statistical quantum optics is carried out. From a suitably defined auxiliary two‐point function we are able to identify the excited modes in the wave field. The relative simplicity of the higher order correlation functions emerge as a byproduct and the conditions under which these are made pure are derived. These results depend in a crucial manner on the notion of coherence indices and of unimodular coherence indices. A new class of approximate expressions for the density operator of a statistical wave field is worked out based on discrete characteristic sets. These are even more economical than the diagonal coherent state representations. An appreciation of the subtleties of quantum theory obtains. Certain implications for the physics of light beams are cited.

Propagation Of Vlf Electromagnetic-Waves In An Idealized Earth-Crust Wave-Guide With Overburden

Theoretical study of propagation characteristics of VLF electromagnetic waves through an idealised parallel-plane earth-crust waveguide with overburden, experimental verification of some of these characteristics with the aid of a model tank and use of range equation reveal the superiority of radio communication between land and a deeply submerged terminal inside a ocean via the earth-crust over direct link communication through the ocean.