Energy bounds for the spinless Salpeter equation: harmonic oscillator

We study the eigenvalues E_{n\ell} of the Salpeter Hamiltonian H = \beta\sqrt(m^2 + p^2) + vr^2, v>0, \beta > 0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple semi-classical formula E = min_{r > 0} {v(P/r)^2 + \beta\sqrt(m^2 + r^2)} provides both upper and lower energy bounds for all the eigenvalues of the problem.Comment: 8 pages, 1 figur

Relativistic N-Boson Systems Bound by Oscillator Pair Potentials

We study the lowest energy E of a relativistic system of N identical bosons bound by harmonic-oscillator pair potentials in three spatial dimensions. In natural units the system has the semirelativistic ``spinless-Salpeter'' Hamiltonian H = \sum_{i=1}^N \sqrt{m^2 + p_i^2} + \sum_{j>i=1}^N gamma |r_i - r_j|^2, gamma > 0. We derive the following energy bounds: E(N) = min_{r>0} [N (m^2 + 2 (N-1) P^2 / (N r^2))^1/2 + N (N-1) gamma r^2 / 2], N \ge 2, where P=1.376 yields a lower bound and P=3/2 yields an upper bound for all N \ge 2. A sharper lower bound is given by the function P = P(mu), where mu = m(N/(gamma(N-1)^2))^(1/3), which makes the formula for E(2) exact: with this choice of P, the bounds coincide for all N \ge 2 in the Schroedinger limit m --> infinity.Comment: v2: A scale analysis of P is now included; this leads to revised energy bounds, which coalesce in the large-m limi

Perturbation expansions for a class of singular potentials

Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page

Coulomb plus power-law potentials in quantum mechanics

We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q > -2 and q \ne 0. We show by envelope theory that the discrete eigenvalues E_{n\ell} of H may be approximated by the semiclassical expression E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}. Values of mu and nu are prescribed which yield upper and lower bounds. Accurate upper bounds are also obtained by use of a trial function of the form, psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure

An Investigation of the Stratigraphy and Tectonics of the Kent Area, Western Connecticut

Guidebook for field trips in Connecticut and south central Massachusetts: New England Intercollegiate Geological Conference 74th annual meeting, University of Connecticut, Storrs Connecticut , October 2 and 3, 1982: Trip P-

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

Duration of antibody response following vaccination against feline immunodeficiency virus

Objectives: Recently, two point-of-care (PoC) feline immunodeficiency virus (FIV) antibody test kits (Witness and Anigen Rapid) were reported as being able to differentiate FIV-vaccinated from FIV-infected cats at a single time point, irrespective of the gap between testing and last vaccination (0–7 years). The aim of the current study was to investigate systematically anti-FIV antibody production over time in response to the recommended primary FIV vaccination series. Methods: First, residual plasma from the original study was tested using a laboratory-based ELISA to determine whether negative results with PoC testing were due to reduced as opposed to absent antibodies to gp40. Second, a prospective study was performed using immunologically naive client-owned kittens and cats given a primary FIV vaccination series using a commercially available inactivated whole cell/inactivated whole virus vaccine (Fel-O-Vax FIV, three subcutaneous injections at 4 week intervals) and tested systematically (up to 11 times) over 6 months, using four commercially available PoC FIV antibody kits (SNAP FIV/FeLV Combo [detects antibodies to p15/p24], Witness FeLV/FIV [gp40], Anigen Rapid FIV/FeLV [p24/gp40] and VetScan FeLV/FIV Rapid [p24]). Results: The laboratory-based ELISA showed cats from the original study vaccinated within the previous 0–15 months had detectable levels of antibodies to gp40, despite testing negative with two kits that use gp40 as a capture antigen (Witness and Anigen Rapid kits). The prospective study showed that antibody testing with SNAP Combo and VetScan Rapid was positive in all cats 2 weeks after the second primary FIV vaccination, and remained positive for the duration of the study (12/12 and 10/12 cats positive, respectively). Antibody testing with Witness and Anigen Rapid was also positive in a high proportion of cats 2 weeks after the second primary FIV vaccination (8/12 and 7/12, respectively), but antibody levels declined below the level of detection in most cats (10/12) by 1 month after the third (final) primary FIV vaccination. All cats tested negative using Witness and Anigen Rapid 6 months after the third primary FIV vaccination. Conclusions and relevance: This study has shown that a primary course of FIV vaccination does not interfere with FIV antibody testing in cats using Witness and Anigen Rapid, provided primary vaccination has not occurred within the previous 6 months. Consequently, Witness and Anigen Rapid antibody test kits can be used reliably to determine FIV infection status at the time of annual booster FIV vaccination to help detect ‘vaccine breakthroughs’ and in cats that have not received a primary course of FIV vaccination within the preceding 6 months. The duration of antibody response following annual booster FIV vaccination and the resulting effect on antibody testing using PoC kits needs to be determined by further research. The mechanism(s) for the variation in FIV antibody test kit performance remains unclear

Asymptotic iteration method for eigenvalue problems

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.Comment: 14 page

Variational analysis for a generalized spiked harmonic oscillator

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.Comment: 15 pages, 1 figur

Semirelativistic stability of N-boson systems bound by 1/r pair potentials

We analyze a system of self-gravitating identical bosons by means of a semirelativistic Hamiltonian comprising the relativistic kinetic energies of the involved particles and added (instantaneous) Newtonian gravitational pair potentials. With the help of an improved lower bound to the bottom of the spectrum of this Hamiltonian, we are able to enlarge the known region for relativistic stability for such boson systems against gravitational collapse and to sharpen the predictions for their maximum stable mass.Comment: 11 pages, considerably enlarged introduction and motivation, remainder of the paper unchange