Eigenvalue bounds for a class of singular potentials in N dimensions

The eigenvalue bounds obtained earlier [J. Phys. A: Math. Gen. 31 (1998) 963] for smooth transformations of the form V(x) = g(x^2) + f(1/x^2) are extended to N-dimensions. In particular a simple formula is derived which bounds the eigenvalues for the spiked harmonic oscillator potential V(x) = x^2 + lambda/x^alpha, alpha > 0, lambda > 0, and is valid for all discrete eigenvalues, arbitrary angular momentum ell, and spatial dimension N.Comment: 10 pages (plain tex with 2 ps figures). J.Phys.A:Math.Gen.(In Press

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

Discrete Spectra of Semirelativistic Hamiltonians

We review various attempts to localize the discrete spectra of semirelativistic Hamiltonians of the form H = \beta \sqrt{m^2 + p^2} + V(r) (w.l.o.g. in three spatial dimensions) as entering, for instance, in the spinless Salpeter equation. Every Hamiltonian in this class of operators consists of the relativistic kinetic energy \beta \sqrt{m^2 + p^2} (where \beta > 0 allows for the possibility of more than one particles of mass m) and a spherically symmetric attractive potential V(r), r = |x|. In general, accurate eigenvalues of a nonlocal Hamiltonian operator can only be found by the use of a numerical approximation procedure. Our main emphasis, however, is on the derivation of rigorous semi-analytical expressions for both upper and lower bounds to the energy levels of such operators. We compare the bounds obtained within different approaches and present relationships existing between the bounds.Comment: 21 pages, 3 figure

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

Gemini-South + FLAMINGOS Demonstration Science: Near-Infrared Spectroscopy of the z=5.77 Quasar SDSS J083643.85+005453.3

We report an infrared 1-1.8 micron (J+H-bands), low-resolution (R=450) spectrogram of the highest-redshift radio-loud quasar currently known, SDSS J083643.85+005453.3, obtained during the spectroscopic commissioning run of the FLAMINGOS multi-object, near-infrared spectrograph at the 8m Gemini-South Observatory. These data show broad emission from both CIV 1549 and CIII] 1909, with strengths comparable to lower-redshift quasar composite spectra. The implication is that there is substantial enrichment of the quasar environment, even at times less than a billion years after the Big Bang. The redshift derived from these features is z = 5.774 +/- 0.003, more accurate and slightly lower than the z = 5.82 reported in the discovery paper based on the partially-absorbed Lyman-alpha emission line. The infrared continuum is significantly redder than lower-redshift quasar composites. Fitting the spectrum from 1.0 to 1.7 microns with a power law f(nu) ~ nu^(-alpha), the derived power law index is alpha = 1.55 compared to the average continuum spectral index = 0.44 derived from the first SDSS composite quasar. Assuming an SMC-like extinction curve, we infer a color excess of E(B-V) = 0.09 +/- 0.01 at the quasar redshift. Only approximately 6% of quasars in the optically-selected Sloan Digital Sky Survey show comparable levels of dust reddening.Comment: 10 pages, 1 figure; to appear in the Astrophysical Journal Letter

Perurbation expansions for the spiked harmonic oscillator and related series involving the gamma function

We study weak-coupling perturbation expansions for the ground-state energy of the Hamiltonian with the generalized spiked harmonic oscillator potential V(x) = Bx^2 + A/x^2 + lambda/x^alpha, and also for the bottoms of the angular momentum subspaces labelled by ell = 0,1,2 ..., in N-dimensions corresponding to the spiked harmonic oscillator potential: V(x) = x^2 + lambda/x^alpha, where alpha is a real positive parameter. A method of Znojil is then applied to obtain closed form expressions for the sums of some infinite series whose terms involve ratios and products of gamma functions.Comment: 9 page

The BTC40 Survey for Quasars at 4.8 < z < 6

The BTC40 Survey for high-redshift quasars is a multicolor search using images obtained with the Big Throughput Camera (BTC) on the CTIO 4-m telescope in V, I, and z filters to search for quasars at redshifts of 4.8 < z < 6. The survey covers 40 sq. deg. in B, V, & I and 36 sq. deg. in z. Limiting magnitudes (3 sigma) reach to V = 24.6, I = 22.9 and z = 22.9. We used the (V-I) vs. (I-z) two-color diagram to select high-redshift quasar candidates from the objects classified as point sources in the imaging data. Follow-up spectroscopy with the AAT and CTIO 4-m telescopes of candidates having I < 21.5 has yielded two quasars with redshifts of z = 4.6 and z = 4.8 as well as four emission line galaxies with z = 0.6. Fainter candidates have been identified down to I = 22 for future spectroscopy on 8-m class telescopes.Comment: 27 pages, 8 figures; Accepted for publication in the Astronomical Journa

General energy bounds for systems of bosons with soft cores

We study a bound system of N identical bosons interacting by model pair potentials of the form V(r) = A sgn(p)r^p + B/r^2, A > 0, B >= 0. By using a variational trial function and the `equivalent 2-body method', we find explicit upper and lower bound formulas for the N-particle ground-state energy in arbitrary spatial dimensions d > 2 for the two cases p = 2 and p = -1. It is demonstrated that the upper bound can be systematically improved with the aid of a special large-N limit in collective field theory

Miocene UHT granulites from Seram, eastern Indonesia: a geochronological-REE study of zircon, monazite and garnet

Peer reviewe