The bicomplex quantum Coulomb potential problem

Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for that purpose is relatively new. This paper provides an analytical solution of the quantum Coulomb potential problem formulated in terms of bicomplex numbers. We define the problem by introducing a bicomplex hamiltonian operator and extending the canonical commutation relations to the form [X_i,P_k] = i_1 hbar xi delta_{ik}, where xi is a bicomplex number. Following Pauli's algebraic method, we find the eigenvalues of the bicomplex hamiltonian. These eigenvalues are also obtained, along with appropriate eigenfunctions, by solving the extension of Schrodinger's time-independent differential equation. Examples of solutions are displayed. There is an orthonormal system of solutions that belongs to a bicomplex Hilbert space.Comment: Clarifications; some figures removed; version to appear in Can. J. Phy

Reactor power systems for manned earth orbital applications

Design requirements for reactor power system of manned earth orbital space statio

Current-induced nuclear-spin activation in a two-dimensional electron gas

Electrically detected nuclear magnetic resonance was studied in detail in a two-dimensional electron gas as a function of current bias and temperature. We show that applying a relatively modest dc-current bias, I_dc ~ 0.5 microAmps, can induce a re-entrant and even enhanced nuclear spin signal compared with the signal obtained under similar thermal equilibrium conditions at zero current bias. Our observations suggest that dynamic nuclear spin polarization by small current flow is possible in a two-dimensional electron gas, allowing for easy manipulation of the nuclear spin by simple switching of a dc current.Comment: 5 pages, 3 fig

Soliton quantization and internal symmetry

We apply the method of collective coordinate quantization to a model of solitons in two spacetime dimensions with a global $U(1)$ symmetry. In particular we consider the dynamics of the charged states associated with rotational excitations of the soliton in the internal space and their interactions with the quanta of the background field (mesons). By solving a system of coupled saddle-point equations we effectively sum all tree-graphs contributing to the one-point Green's function of the meson field in the background of a rotating soliton. We find that the resulting one-point function evaluated between soliton states of definite $U(1)$ charge exhibits a pole on the meson mass shell and we extract the corresponding S-matrix element for the decay of an excited state via the emission of a single meson using the standard LSZ reduction formula. This S-matrix element has a natural interpretation in terms of an effective Lagrangian for the charged soliton states with an explicit Yukawa coupling to the meson field. We calculate the leading-order semi-classical decay width of the excited soliton states discuss the consequences of these results for the hadronic decay of the $\Delta$ resonance in the Skyrme model.Comment: 23 pages, LA-UR-93-299

Domain Walls in a FRW Universe

We solve the equations of motion for a scalar field with domain wall boundary conditions in a Friedmann-Robertson-Walker (FRW) spacetime. We find (in agreement with Basu and Vilenkin) that no domain wall solutions exist in de Sitter spacetime for h = H/m >= 1/2, where H is the Hubble parameter and m is the scalar mass. In the general FRW case we develop a systematic perturbative expansion in h to arrive at an approximate solution to the field equations. We calculate the energy momentum tensor of the domain wall configuration, and show that the energy density can become negative at the core of the defect for some values of the non-minimal coupling parameter xi. We develop a translationally invariant theory for fluctuations of the wall, obtain the effective Lagrangian for these fluctuations, and quantize them using the Bunch-Davies vacuum in the de Sitter case. Unlike previous analyses, we find that the fluctuations act as zero-mass (as opposed to tachyonic) modes. This allows us to calculate the distortion and the normal-normal correlators for the surface. The normal-normal correlator decreases logarithmically with the distance between points for large times and distances, indicating that the interface becomes rougher than in Minkowski spacetime.Comment: 23 pages, LaTeX, 7 figures using epsf.tex. Now auto-generates P

PARAMETERS OF BALL RELEASE IN WHEELCHAIR BASKETBALL FREE THROW SHOOTING

The purpose of this study was to identify the relationship between ball release parameters and player classification in wheelchair basketball free throw shooting. Utilizing three-dimensional (3D) video data collected during international competition, parameters of ball release associated with performance of the dean swish were examined. Significant differences were identified between the four player classes. The upper classes (3 & 4) tended to release the ball from a greater height, with less speed and a smaller angle of projection. The lower classes used a technique that demanded greater accuracy, but still managed to achieve free throw shooting percentages similar to the upper classes (3 & 4) who did not appear to utilize their height advantage

Free fields via canonical transformations of matter-coupled 2D dilaton gravity models

It is shown that the 1+1-dimensional matter-coupled Jackiw-Teitelboim model and the model with an exponential potential can be converted by means of appropriate canonical transformations into a bosonic string theory propagating on a flat target space with an indefinite signature. This makes it possible to consistently quantize these models in the functional Schroedinger representation thus generalizing recent results on CGHS theory.Comment: 15 pages, Late

WW--geometry of the Toda systems associated with non-exceptional simple Lie algebras

The present paper describes the $W$--geometry of the Abelian finite non-periodic (conformal) Toda systems associated with the $B,C$ and $D$ series of the simple Lie algebras endowed with the canonical gradation. The principal tool here is a generalization of the classical Pl\"ucker embedding of the $A$-case to the flag manifolds associated with the fundamental representations of $B_n$, $C_n$ and $D_n$, and a direct proof that the corresponding K\"ahler potentials satisfy the system of two--dimensional finite non-periodic (conformal) Toda equations. It is shown that the $W$--geometry of the type mentioned above coincide with the differential geometry of special holomorphic (W) surfaces in target spaces which are submanifolds (quadrics) of $CP^N$ with appropriate choices of $N$. In addition, these W-surfaces are defined to satisfy quadratic holomorphic differential conditions that ensure consistency of the generalized Pl\"ucker embedding. These conditions are automatically fulfiled when Toda equations hold.Comment: 30 pages, no figur

THE EFFECT OF WRIST RESTRAINTS ON WHEELING BIOMECHANICS

High intracarpal pressures created by hyperextension of the wrist during wheelchair propulsion is a suggested cause of median nerve dysfunction at the wrist/hand (Burnham & Steadward, 1994). An injury survey conducted by Burnham, Higgins & Steadward (1994) found that the wrist and hand were the most common sites of injury reported by wheelchair basketball players. The purpose of this study was to assess whether various forms of hand/wrist protection (visco-elastic padded glove, wrist splint, glove and splint) could effectively reduce the hyperextension seen at the wrist during wheelchair propulsion, thus potentially reducing the conditions predisposing to carpal tunnel syndrome. In addition, an evaluation of the various forms of hand/wrist protection and their effects on wheeling mechanics was also undertaken. The wheeling performances of thirteen subjects with prior wheeling experience were recorded using two SVHS videorecorders positioned to obtain a front and side view. Each subject propelled a standard wheelchair basketball chair mounted to a set of wheelchair rollers under four different conditions (no splint, visco-elastic padded glove on the palms, wrist splint, and glove and splint together). Under each of the conditions the subjects wheeled for thirty seconds both at their average speed and at their maximum speed. Reflective markers were placed on the joint centers of the shoulder and elbow, on the styloid processes of the radius and ulna, and on the distal ends of the 2nd and 5th metacarpals of the right limb to facilitate subsequent digitizing. Twelve points surrounding the activity space were filmed prior to testing and later utilized for calibration using the DLT method for three-dimensional coordinate data reconstruction, followed by smoothing of the data using a cubic spline. Three-dimensional joint angular displacement-time histories for the elbow and wrist were determined using the 3D coordinate data and the dot product identity. Data were analyzed using an one way AN OVA followed by Scheffe post hoc comparisons where appropriate. No differences were found to be significant between the conditions for the elbow angle, however significant differences were revealed for the wrist extension and wrist range of motion angles. Both splint conditions (splint, glove &splint) were significantly different from the non-restraint conditions (no splint, glove). The data suggest that the splints significantly reduced the amount of wrist extension as compared to the no restraint conditions. No significant differences were found between the conditions for maximum wheeling speed. Within the limitations of this study, it can be concluded that the wrist restraints significantly reduced wrist extension during wheeling and that the restraints did not significantly affect wheeling mechanics as suggested by the consistent elbow-angle time histories and wheeling speeds. REFERENCES Burnham, R & Steadward, R (1994). Upper extremity peripheral nerve entrapments among wheelchair athletes: prevalence, location, and risk factors. Archives of Physical Medicine and Rehabilitation, 75, 519 524. Burnham, R, Higgins, J. & Steadward, R. (1994). Wheelchair basketball injuries. Palaestra, 10(2), 43-49