Exact and approximate solutions of Schrödinger’s equation for a class of trigonometric potentials

The asymptotic iteration method is used to find exact and approximate solutions of Schrödinger’s equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent). Analytic and approximate solutions are obtained by first using a coordinate transformation to reduce the Schrödinger equation to a second-order differential equation with an appropriate form. The asymptotic iteration method is also employed indirectly to obtain the terms in perturbation expansions, both for the energies and for the corresponding eigenfunctions.     

Observation of triplet doubly excited states in single photon excitation from ground state helium

We have observed, for the first time, LS-forbidden triplet doubly excited states, in single photon excitation of ground state helium, below the second ionization threshold. These states are identified as (3)D(o) and (3)P(o) and their excitation is due to spin-orbit interaction that mixes them with the optically allowed (1)P(o) states. This observation is possible due to the very high efficiency in detecting metastable atoms created after the fluorescence decay of the doubly excited states, and the new capabilities of third generation synchrotron vacuum ultraviolet sources with high resolution beam lines.     

New perspective on cosmic coincidence problems

Cosmological data suggest that we live in an interesting period in the history of the universe when rho(Lambda) approximately rho(M) approximately rho(R). The occurrence of any epoch with such a "triple coincidence" is puzzling, while the question of why we happen to live during this special epoch is the "Why now?" problem. We introduce a framework which makes the triple coincidence inevitable; furthermore, the "Why now?" problem is transformed and greatly ameliorated. The framework assumes that the only relevant mass scales are the electroweak scale M(EW), and the Planck scale M(Pl) and requires rho(1/4)(Lambda) approximately M(2)(EW)/M(Pl) parametrically. Assuming that the true vacuum energy vanishes, we present a simple model, where a false vacuum energy yields a cosmological constant of this form.     

Asynchronous phase-modulated optical fiber-ring buffer

We investigate the dynamics of a 5-Gbit/s packet of ones and zeros loaded into a 0.5-kbit, phase-modulated optical fiber-ring buffer. A new mode of operation is explored in which the cavity length of the buffer is slightly detuned from the frequency driving the phase modulator. We examine the conditions for successful packet loading and the packet storage behavior. In addition, relaxation oscillations, which affected the storage time of previous high-speed optical ring buffers, are nearly eliminated with a cw holding beam, and significantly enhanced storage times are obtained.     

Activity interference and noise annoyance

Debate continues over differences in the dose-response functions used to predict the annoyance at different sources of transportation noise. This debate reflects the lack of an accepted model of noise annoyance in residential communities. In this paper a model is proposed which is focussed on activity interference as a central component mediating the relationship between noise exposure and annoyance. This model represents a departure from earlier models in two important respects. First, single event noise levels (e.g., maximum levels, sound exposure level) constitute the noise exposure variables in place of long-term energy equivalent measures (e.g., 24-hour L_eq or L_dn). Second, the relationships within the model are expressed as probabilistic rather than deterministic equations. The model has been tested by using acoustical and social survey data collected at 57 sites in the Toronto region exposed to aircraft, road traffic or train noise. Logit analysis was used to estimate two sets of equations. The first predicts the probability of activity interference as a function of event noise level. Four types of interference are included: indoor speech, outdoor speech, difficulty getting to sleep and awakening. The second set predicts the probability of annoyance as a function of the combination of activity interferences. From the first set of equations, it was possible to estimate a function for indoor speech interference only. In this case, the maximum event level was the strongest predictor. The lack of significant results for the other types of interference is explained by the limitations of the data. The same function predicts indoor speech interference for all three sources—road, rail and aircraft noise. The results for the second set of equations show strong relationships between activity interference and the probability of annoyance. Again, the parameters of the logit equations are similar for the three sources. A trial application of the model predicts a higher probability of annoyance for aircraft than for road traffic situations with the same 24-hour L_eq. This result suggests that the model may account for previously reported source differences in annoyance.     

Intensity convolutions of CARS spectra

A derivation of the convolution integral for finite bandwidth pump and Stokes sources in CARS is given. The resulting “partially coherent” convolution confirms previously published results, and is compared to the widely used incoherent treatment. The effect of intensity convolution choice on multiplex CARS thermometry is evaluated by reducing N₂ data taken in an ethylene-air diffusion flame. N₂ CARS thermometry using multimode pumps is ordinarily not very sensitive to convolution.     

Defect dominated conductivity in Zn3P2

The electrical resistivity and Hall coefficient of Zn₃P₂ have been measured for single crystal and thin polycrystalline film samples which were annealed over a range of equilibrium vapor compositions and temperatures. The room temperature electrical resistivity of single crystal samples annealed at 573 K varied from approximately 10⁵Ω-cm for single crystals heated in equilibrium with zinc to 10 Ω-cm for those annealed in a phosphorus rich ambient. Hall measurements indicate that a variation in carrier concentration is responsible for these changes. The experimentally observed dependence of carrier concentration [h° ], (cm^?3) on phosphorus pressure is given by [h°] = 1.32 · 10¹⁶ [p(P₄)]^0.13 for samples annealed at 573 K. The experimentally determined pressure dependence is in good agreement with a model based on phosphorus interstitials acting as acceptors. The pressure and temperature dependence of the carrier concentration yield the equilibrium constant K_I for the formation of interstitial phosphorus defects according to the reaction

$\text{1}\text{4}\text{P}{}_4\text{→ P′}{}_{\mathrm{i}}\text{+ h°}$

where

$\text{K}{}_{\mathrm{I}}\text{= 10}{}^{\mathrm{42.4\; \pm \; 2}}\text{cm}{}^{\mathrm{?6}}\text{torr}{}^{0.25}\text{[p(P}{}_4\text{)]}{}^{\mathrm{?0.25}}\text{exp(?1.18}\text{ev}\text{kT}\text{)}$

. The accommodation of phosphorus interstitials is discussed in light of the crystal structure of Zn₃P₂.