S. Waldenstrøm

The overlap integrals of two harmonic-oscillator wavefunctions: some remarks on originals and reproductions

Abstract The problem, treated in several papers published during the last decade, of finding a compact expression for the overlap integral of the wavefunctions of two displaced and distorted harmonic oscillators was solved more than twenty years ago by Ansbacher; we recall the contributions made by two other neglected, contemporaneous authors. Wagner and Koide.

Thirteen-moment solution of the steady-state fokker—planck equation for Brownian motion in a homogeneous medium occupying the region bounded internally by an absorbing sphere

Abstract The steady, centrally symmetric motion of Brownian particles in a homogeneous medium occupying the region bounded internally by an absorbing sphere of radius R is considered. The distribution function of the particles, assumed to obey the generalized fokker—Planck equation, is found (in three successive approximations) by applying Grads method of moments, which consists in expanding the distribution function in Hermitean tensors and truncating the series after the term of N th order. Approximations up to and including the so-called 13-moment approximation (corresponding to N = 1, 2,and3) are studied, and a previous 13-moment analysis is criticized; it is stressed that the results furnished by the N th-order approximation are valid to O ( Λ/ R ) N , where Λ is the velocity persistence length.

Brownian Motion Description of Heat Conduction by Phonons

A new equation, rooted in the theory of Brownian motion, is proposed for describing heat conduction by phonons. Though a finite speed of propagation is a built-in feature of the equation, it does not give rise to an inauthentic wave front that results from the application of the hyperbolic heat equation (of Cattaneo). Even a simplified, analytically tractable version of the equation yields results close to those found by solving, through more elaborate means, the equation of phonon radiative transfer. An explanation is given as to why both Brownian motion and its inverse (radiative transfer) provide equally serviceable paradigms for phonon-mediated heat conduction.

Symmetric random walk on a regular lattice with an elastic barrier: diffusion equation and the boundary condition

Abstract We examine here the symmetric random-walk model in which a particle can jump only to adjacent sites on a regular lattice, and discuss, in the light of the works of Chandrasekhar, Goodrich, van Kampen, and Oppenheim, the reduction of the problem of random walk in the presence of an elastic barner to a boundary value problem.

On describing the steady absorption of brownian particles by a restricted random walk

Abstract This paper is concerned with idealizing brownian motion as a random walk, using the diffusion equation, and finding the boundary condition at an absorbing surface - all with an eye towards chemical kinetics. Three models of random walk (due to Smoluchowski, Fermi, and Lorentz) are considered, and it is concluded that the lorentzian model is the most appropriate.

Fractional revival of wave packets in an infinite square well: a Fourier perspective

Fractional revivals of wave packets in an infinite square well are scrutinized with a viewpoint rooted in Fourier analysis, and a compact relation, expressing the wavefunction Ψ(x,t) for certain values of t in terms of spatially displaced copies of Ψ(x,0), is derived without appealing to a classical analogy; conditions for the appearance of an interference pattern in a plot of the position probability density of a wave packet are deduced, along with related results obtained previously from different considerations, with minimal effort. The specific case of a packet of Gaussian shape is analysed in greater detail to provide concrete illustrations of fractional revivals with or without interference between overlapping copies of wave packets, depending on whether a finite value of the so-called classical time can or cannot be assigned to the wave packet.

A neglected aspect of the pulsating Gaussian wave packet

The dissipation of a highly localized harmonic oscillator wave packet of Gaussian form and its subsequent revival (and the revival of wave packets in an infinite square well) are discussed; these examples are evocative of the echoes encountered in many domains of physics.

Engineering & Laboratory Notes Measurement of Refractive Indices of Prismatic Materials

The purpose of this work is to describe the advantages of a simple alternative to the minimum-deviation and other methods used to determine refractive indices of prism-shaped specimens.