I. Quantum mechanics of one-dimensional two-particle models. II. A quantum mechanical treatment of inelastic collisions

Part I

Solutions of Schrödinger’s equation for system of two particles bound in various stationary one-dimensional potential wells and repelling each other with a Coulomb force are obtained by the method of finite differences. The general properties of such systems are worked out in detail for the case of two electrons in an infinite square well. For small well widths (1-10 a.u.) the energy levels lie above those of the noninteresting particle model by as much as a factor of 4, although excitation energies are only half again as great. The analytical form of the solutions is obtained and it is shown that every eigenstate is doubly degenerate due to the “pathological” nature of the one-dimensional Coulomb potential. This degeneracy is verified numerically by the finite-difference method. The properties of the square-well system are compared with those of the free-electron and hard-sphere models; perturbation and variational treatments are also carried out using the hard-sphere Hamiltonian as a zeroth-order approximation. The lowest several finite-difference eigenvalues converge from below with decreasing mesh size to energies below those of the “best” linear variational function consisting of hard-sphere eigenfunctions. The finite-difference solutions in general yield expectation values and matrix elements as accurate as those obtained using the “best” variational function.

The system of two electrons in a parabolic well is also treated by finite differences. In this system it is possible to separate the center-of-mass motion and hence to effect a considerable numerical simplification. It is shown that the pathological one-dimensional Coulomb potential gives rise to doubly degenerate eigenstates for the parabolic well in exactly the same manner as for the infinite square well.

Part II

A general method of treating inelastic collisions quantum mechanically is developed and applied to several one-dimensional models. The formalism is first developed for nonreactive “vibrational” excitations of a bound system by an incident free particle. It is then extended to treat simple exchange reactions of the form A + BC →AB + C. The method consists essentially of finding a set of linearly independent solutions of the Schrödinger equation such that each solution of the set satisfies a distinct, yet arbitrary boundary condition specified in the asymptotic region. These linearly independent solutions are then combined to form a total scattering wavefunction having the correct asymptotic form. The method of finite differences is used to determine the linearly independent functions.

The theory is applied to the impulsive collision of a free particle with a particle bound in (1) an infinite square well and (2) a parabolic well. Calculated transition probabilities agree well with previously obtained values.

Several models for the exchange reaction involving three identical particles are also treated: (1) infinite-square-well potential surface, in which all three particles interact as hard spheres and each two-particle subsystem (i.e. BC and AB) is bound by an attractive infinite-square-well potential; (2) truncated parabolic potential surface, in which the two-particle subsystems are bound by a harmonic oscillator potential which becomes infinite for interparticle separations greater than a certain value; (3) parabolic (untruncated) surface. Although there are no published values with which to compare our reaction probabilities, several independent checks on internal consistency indicate that the results are reliable.

Treading in Mortimer's footsteps: the geochemical cycling of iron and manganese in Esthwaite water

A study of the geochemical cycling of iron and manganese in a seasonally stratified lake, Esthwaite water is described. This work is based on speculative ideas on environmental redox chemistry of iron which were proposed by C.H. Mortimer in the 1940's. These observations have been verified and some speculations confirmed, along with a new understanding of the manganese cycle, and detailed information on the particulate forms of both iron and manganese. Details on the mechanisms and transformations of iron have also emerged.

Aspects of the washout of salmonid eggs. 4. Effects of a standard mechanical shock, applied at different stage of development, upon survival and development of eggs of brown trout (Salmo trutta L.)

It is generally accepted by fish culturists that salmonid eggs are sensitive to mechanical shock and that the sensitivity varies with the stage of development of the eggs. In general, the period of greatest sensitivity is thought to occur between fertilization and ”eyeing”. However, it is reasonable to expect that, during a period (perhaps of several hours) following fertilization, sensitivity will be low because in nature during this period the eggs may be subject to some mechanical shock caused by the parent fish covering them with gravel. In 1983-4 and 1984-5 experiments were performed on brown trout (Salmo trutta L.) eggs to examine the effect of a standard mechanical shock (c. 2,500 eggs in 1983-4 and c. 8,400 eggs in 1984-5) at various stages of development upon survival to hatching and time of hatching.The results of these experiments are reported in this study.

Specklegram in a grapefruit fiber and its response to external mechanical disturbance in a single-multiple-single mode fiber structure

Specklegram in multimode fiber has successfully been used as a sensor for detecting mechanical disturbance. Speckles in a multimode pure silica grapefruit fiber are observed and compared to that of a step-index multimode fiber, showing different features between them. The sensitivities to external disturbance of two kinds of fiber were measured, based on single-multiple-single mode (SMS) fiber structure. Experimental results show that the grapefruit fiber shows higher sensitivity than does the step-index multimode fiber. The transmission spectrum of the grapefruit fiber was measured as well, showing some oscillation features that are significantly different from that of a step-index multimode fiber. The experiments may provide suggestions to understand the mechanisms of light propagation in grapefruit fibers. (D 2008 Optical Society of America.

Study of polymer thermal and mechanical properties using a fiber Bragg grating thermal sensor

A simple and practical method for the study of polymer thermal and mechanical properties using a fiber Bragg grating (FBG) sensor is presented for the first time, in which the FBG is embedded in a typical epoxy polymer. By measuring the sensitivity change of the FBG sensor, changes of the thermal-mechanical properties of the polymer with temperature and pressure can be measured. The experimental results show that this technique is capable of providing continuous in-line monitoring such properties with high sensitivity during transformation between the glassy state and the rubbery state of a polymer within the temperature and pressure range of 20 to 180 C and 0 to 15 MPa. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

NANOPARTICLE REINFORCEMENT OF FERROUS ALLOYS: WETTABILITY AND MECHANICAL PROPERTIES

El refuerzo de matrices férricascon una fina dispersión de partículas nanométricas permite mejorar la dureza, resistencia mecánica e incluso permitiría mejorar la tenacidad del material al afinar el tamaño de grano.

Study of polymer thermal and mechanical properties using a fiber Bragg grating thermal sensor

A simple and practical method for the study of polymer thermal and mechanical properties using a fiber Bragg grating (FBG) sensor is presented for the first time, in which the FBG is embedded in a typical epoxy polymer. By measuring the sensitivity change of the FBG sensor, changes of the thermal-mechanical properties of the polymer with temperature and pressure can be measured. The experimental results show that this technique is capable of providing continuous in-line monitoring such properties with high sensitivity during transformation between the glassy state and the rubbery state of a polymer within the temperature and pressure range of 20 to 180 C and 0 to 15 MPa. (c) 2007 Society of Photo-Optical Instrumentation Engineers.