Energies and wave functions for a soft-core Coulomb potential

For the family of model soft Coulomb potentials represented by V(r) = -\frac{Z}{(r^q+\beta^q)^{\frac{1}{q}}}, with the parameters Z>0, \beta>0, q \ge 1, it is shown analytically that the potentials and eigenvalues, E_{\nu\ell}, are monotonic in each parameter. The potential envelope method is applied to obtain approximate analytic estimates in terms of the known exact spectra for pure power potentials. For the case q =1, the Asymptotic Iteration Method is used to find exact analytic results for the eigenvalues E_{\nu\ell} and corresponding wave functions, expressed in terms of Z and \beta. A proof is presented establishing the general concavity of the scaled electron density near the nucleus resulting from the truncated potentials for all q. Based on an analysis of extensive numerical calculations, it is conjectured that the crossing between the pair of states [(\nu,\ell),(\nu',\ell')], is given by the condition \nu'\geq (\nu+1) and \ell' \geq (\ell+3). The significance of these results for the interaction of an intense laser field with an atom is pointed out. Differences in the observed level-crossing effects between the soft potentials and the hydrogen atom confined inside an impenetrable sphere are discussed.Comment: 13 pages, 5 figures, title change, minor revision

Failure Is an Option: Impediments to Short Selling and Options Prices

Regulations allow market makers to short sell without borrowing stock, and the transactions of a major options market maker show that in most hard-to-borrow situations, it chooses not to borrow and instead fails to deliver stock to its buyers. A part of the value of failing passes through to options prices: when failing is cheaper than borrowing, the relation between borrowing costs and options prices is significantly weaker. The remaining value is profit to the market maker, and its ability to profit despite competition between market makers appears to result from the cost advantage of larger market makers

Spectral characteristics for a spherically confined -1/r + br^2 potential

We consider the analytical properties of the eigenspectrum generated by a class of central potentials given by V(r) = -a/r + br^2, b>0. In particular, scaling, monotonicity, and energy bounds are discussed. The potential $V(r)$ is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical boundary of radius R. With the aid of the asymptotic iteration method, several exact analytic results are obtained which exhibit the parametric dependence of energy on a, b, and R, under certain constraints. More general spectral characteristics are identified by use of a combination of analytical properties and accurate numerical calculations of the energies, obtained by both the generalized pseudo-spectral method, and the asymptotic iteration method. The experimental significance of the results for both the free and confined potential V(r) cases are discussed.Comment: 16 pages, 4 figure

Multimodal Vulvar and Peripheral Sensitivity Among Women With Vulvodynia: A Case–Control Study

OBJECTIVE: To assess differences in vulvar and peripheral sensitivity between women with and without vulvodynia. METHODS: Women with vulvodynia (n = 41) and age-matched controls (n = 43) seen in the outpatient setting were evaluated via surveys, clinical examination, and multimodal sensory testing (pressure, heat, cold, vibration, and electrical stimulation). The relationships between sensitivity to various sensory modalities and case/control status, as well as by vulvodynia subgroups, were assessed using logistic regression. RESULTS: Women with vulvodynia were more sensitive to pressure and to electrical stimuli than were control women at the vulva (median, 22 vs 230 g and 0.495 vs 0.769 mA, respectively; P 0.025). Those reporting spontaneous pain versus provoked pain had greater pressure sensitivity to the thumb (median, 1850 vs 2690 g; P = 0.020) and greater electrical sensitivity at the introitus (0.450 vs 0.608 mA; P = 0.011), and those with primary versus secondary vulvodynia had substantially greater pressure sensitivity to the thumb (median, 2438 vs 3125 g, P = 0.004). However, having localized versus generalized vulvodynia was not associated with differences in pressure or electrical sensitivity. CONCLUSIONS: Sensitivities to pressure and electrical stimuli are greater among vulvodynia cases than among controls and support 2 previously defined subgroups-those reporting spontaneous pain versus those whose pain only occurred when provoked, and those with primary versus secondary vulvodynia

Geometric spectral inversion for singular potentials

The function E = F(v) expresses the dependence of a discrete eigenvalue E of the Schroedinger Hamiltonian H = -\Delta + vf(r) on the coupling parameter v. We use envelope theory to generate a functional sequence \{f^{[k]}(r)\} to reconstruct f(r) from F(v) starting from a seed potential f^{[0]}(r). In the power-law or log cases the inversion can be effected analytically and is complete in just two steps. In other cases convergence is observed numerically. To provide concrete illustrations of the inversion method it is first applied to the Hulth\'en potential, and it is then used to invert spectral data generated by singular potentials with shapes of the form f(r) = -a/r + b\sgn(q)r^q and f(r) = -a/r + b\ln(r), a, b > 0. For the class of attractive central potentials with shapes f(r) = g(r)/r, with g(0)< 0 and g'(r)\ge 0, we prove that the ground-state energy curve F(v) determines f(r) uniquely.Comment: 13 pages, 5 figure

Measuring nonuse damages using contingent valuation

This second edition of Measuring Nonuse Damages Using Conjoint Valuation is essentially a reprint of a 1992 monograph that has been in steady demand since its original appearance. The RTI Press edition, which is intended to meet continued inquiries and requests for the monograph, contains a Foreword and a Preface to the second edition that put the original work into historical perspective. These studies of ways to value stated preferences, as applied then to the Exxon Valdez oil spill, continue to be a timely and still-rigorous examination of such methods; even with the passage of time and statistical advances from the past two decades, the conclusions and insights as to whether and how these techniques might still be employed in valuing use or nonuse losses from similar events remain valid.Publishe

Robotic Laser-Adaptive-Optics Imaging of 715 Kepler Exoplanet Candidates using Robo-AO

The Robo-AO Kepler Planetary Candidate Survey is designed to observe every Kepler planet candidate host star with laser adaptive optics imaging to search for blended nearby stars, which may be physically associated companions and/or responsible for transit false positives. In this paper we present the results from the 2012 observing season, searching for stars close to 715 representative Kepler planet candidate hosts. We find 53 companions, 44 of which are new discoveries. We detail the Robo-AO survey data reduction methods including a method of using the large ensemble of target observations as mutual point-spread-function references, along with a new automated companion-detection algorithm designed for large adaptive optics surveys. Our survey is sensitive to objects from 0.15" to 2.5" separation, with contrast ratios up to delta-m~6. We measure an overall nearby-star-probability for Kepler planet candidates of 7.4% +/- 1.0%, and calculate the effects of each detected nearby star on the Kepler-measured planetary radius. We discuss several KOIs of particular interest, including KOI-191 and KOI-1151, which are both multi-planet systems with detected stellar companions whose unusual planetary system architecture might be best explained if they are "coincident multiple" systems, with several transiting planets shared between the two stars. Finally, we detect 2.6-sigma evidence for <15d-period giant planets being 2-3 times more likely be found in wide stellar binaries than smaller close-in planets and all sizes of further-out planets.Comment: Accepted by ApJ. Minor updates & improved statistical analysis; no changes to results. 15 pages, 13 figure

Scattering and self-adjoint extensions of the Aharonov-Bohm hamiltonian

We consider the hamiltonian operator associated with planar sec- tions of infinitely long cylindrical solenoids and with a homogeneous magnetic field in their interior. First, in the Sobolev space $\mathcal H^2$, we characterize all generalized boundary conditions on the solenoid bor- der compatible with quantum mechanics, i.e., the boundary conditions so that the corresponding hamiltonian operators are self-adjoint. Then we study and compare the scattering of the most usual boundary con- ditions, that is, Dirichlet, Neumann and Robin.Comment: 40 pages, 5 figure