Spectrum of One-Dimensional Anharmonic Oscillators

We use a power-series expansion to calculate the eigenvalues of anharmonic oscillators bounded by two infinite walls. We show that for large finite values of the separation of the walls, the calculated eigenvalues are of the same high accuracy as the values recently obtained for the unbounded case by the inner-product quantization method. We also apply our method to the Morse potential. The eigenvalues obtained in this case are in excellent agreement with the exact values for the unbounded Morse potential.Comment: 11 pages, 5 figures, 4 tables; there are changes to match the version published in Can. J. Phy

Exercise during pregnancy. A narrative review asking: What do we know?

Although there is no consensus as to whether exercise is beneficial during pregnancy, most studies report it poses no risk to either the mother or the fetus, and many suggest it to be beneficial to both. This review, which examines the evidence available, also reveals the many differences in study design followed, the type of exercise undertaken and the variables measured, which make it difficult to compare results. Advances in our understanding of the effects of exercise during pregnancy might best be made by undertaking randomised clinical trials with standardised protocols. However, most of the studies examining the relationship between exercise and pregnancy report no complications on maternal or fetal well-being. This is also in line with recent review studies advising that the pregnant population without obstetric contraindications should be encouraged to exercise during pregnancy. Therefore, the results of the present review stimulate those responsible for the healthcare of the pregnant woman to recommend moderate exercise throughout pregnancy without risk to maternal and fetal health

Magnetothermal instabilities in magnetized anisotropic plasmas

Using the transport equations for an ideal anisotropic collisionless plasma derived from the Vlasov equation by the 16-moment method, we analyse the influence of pressure anisotropy exhibited by collisionless magnetized plasmas on the magnetothermal (MTI) and heat-flux-driven buoyancy (HBI) instabilities. We calculate the dispersion relation and the growth rates for these instabilities in the presence of a background heat flux and for configurations with static pressure anisotropy, finding that when the frequency at which heat conduction acts is much larger than any other frequency in the system (i.e. weak magnetic field) the pressure anisotropy has no effect on the MTI/HBI, provided the degree of anisotropy is small. In contrast, when this ordering of timescales does not apply the instability criteria depend on pressure anisotropy. Specifically, the growth time of the instabilities in the anisotropic case can be almost one order of magnitude smaller than its isotropic counterpart. We conclude that in plasmas where pressure anisotropy is present the MTI/HBI are modified. However, in environments with low magnetic fields and small anisotropy such as the ICM the results obtained from the 16-moment equations under the approximations considered are similar to those obtained from ideal MHD.Comment: v3: 16 pages, 2 figures, fixed typos, added references and a final note on related wor

Any ll-state solutions of the Hulth\'en potential by the asymptotic iteration method

In this article, we present the analytical solution of the radial Schr\"{o}dinger equation for the Hulth\'{e}n potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any $l$ states. We obtain the energy eigenvalues and the corresponding eigenfunctions for different screening parameters. The wave functions are physical and energy eigenvalues are in good agreement with the results obtained by other methods for different $\delta$ values. In order to demonstrate this, the results of the asymptotic iteration method are compared with the results of the supersymmetry, the numerical integration, the variational and the shifted 1/N expansion methods.Comment: 14 pages and 1 figur

On the dilaton and the axion potentials

We extend the Vecchia-Veneziano-Witten (VVW) model of QCD in the chiral limit and for large colour number $N_c$, by introducing an effective dilaton-gluon coupling from which we derive both the axion and dilaton potentials. Furthermore, using a string inspired model, we determine a new interquark potential as a perturbative series in terms of the interquark distance $r$. Our potential goes beyond Dick one obtained in [8] and shares the same features as the Bian-Huang-Shen potential $V_{BHS}$ which depends only on odd powers of $r$ [22].Comment: 15 pages, Late

Polarization of tightly focused laser beams

The polarization properties of monochromatic light beams are studied. In contrast to the idealization of an electromagnetic plane wave, finite beams which are everywhere linearly polarized in the same direction do not exist. Neither do beams which are everywhere circularly polarized in a fixed plane. It is also shown that transversely finite beams cannot be purely transverse in both their electric and magnetic vectors, and that their electromagnetic energy travels at less than c. The electric and magnetic fields in an electromagnetic beam have different polarization properties in general, but there exists a class of steady beams in which the electric and magnetic polarizations are the same (and in which energy density and energy flux are independent of time). Examples are given of exactly and approximately linearly polarized beams, and of approximately circularly polarized beams.Comment: 9 pages, 6 figure

The flow of plasma in the solar terrestrial environment

The overall goal of our NASA Theory Program was to study the coupling, time delays, and feedback mechanisms between the various regions of the solar-terrestrial system in a self-consistent, quantitative manner. To accomplish this goal, it will eventually be necessary to have time-dependent macroscopic models of the different regions of the solar-terrestrial system and we are continually working toward this goal. However, with the funding from this NASA program, we concentrated on the near-earth plasma environment, including the ionosphere, the plasmasphere, and the polar wind. In this area, we developed unique global models that allowed us to study the coupling between the different regions. These results are highlighted in the next section. Another important aspect of our NASA Theory Program concerned the effect that localized 'structure' had on the macroscopic flow in the ionosphere, plasmasphere, thermosphere, and polar wind. The localized structure can be created by structured magnetospheric inputs (i.e., structured plasma convection, particle precipitation or Birkland current patterns) or time variations in these input due to storms and substorms. Also, some of the plasma flows that we predicted with our macroscopic models could be unstable, and another one of our goals was to examine the stability of our predicted flows. Because time-dependent, three-dimensional numerical models of the solar-terrestrial environment generally require extensive computer resources, they are usually based on relatively simple mathematical formulations (i.e., simple MHD or hydrodynamic formulations). Therefore, another goal of our NASA Theory Program was to study the conditions under which various mathematical formulations can be applied to specific solar-terrestrial regions. This could involve a detailed comparison of kinetic, semi-kinetic, and hydrodynamic predictions for a given polar wind scenario or it could involve the comparison of a small-scale particle-in-cell (PIC) simulation of a plasma expansion event with a similar macroscopic expansion event. The different mathematical formulations have different strengths and weaknesses and a careful comparison of model predictions for similar geophysical situations provides insight into when the various models can be used with confidence