71,738 research outputs found
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
Discrete spectra of semirelativistic Hamiltonians from envelope theory
We analyze the (discrete) spectrum of the semirelativistic
``spinless-Salpeter'' Hamiltonian H = \beta \sqrt{m^2 + p^2} + V(r), beta > 0,
where V(r) represents an attractive, spherically symmetric potential in three
dimensions. In order to locate the eigenvalues of H, we extend the ``envelope
theory,'' originally formulated only for nonrelativistic Schroedinger
operators, to the case of Hamiltonians H involving the relativistic
kinetic-energy operator. If V(r) is a convex transformation of the Coulomb
potential -1/r and a concave transformation of the harmonic-oscillator
potential r^2, both upper and lower bounds on the discrete eigenvalues of H can
be constructed, which may all be expressed in the form E = min_{r>0} [ \beta
\sqrt{m^2 + P^2/r^2} + V(r) ] for suitable values of the numbers P here
provided. At the critical point, the relative growth to the Coulomb potential
h(r) = -1/r must be bounded by dV/dh < 2 \beta/\pi.Comment: 20 pages, 2 tables, 4 figure
Determination of hydroxyl content in impure magnesium oxide
Three-step thermal process quantitatively determines the hydroxyl content in samples of magnesium oxide. Analytical method can be adapted to large-scale production of hydroxyl-free magnesium oxide
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
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
Recirculation effects produced by a pair of heated jets impinging on a ground plane
Exhaust recirculation effects produced by two heated jets impinging on ground plan
Closed-form sums for some perturbation series involving associated Laguerre polynomials
Infinite series sum_{n=1}^infty {(alpha/2)_n / (n n!)}_1F_1(-n, gamma, x^2),
where_1F_1(-n, gamma, x^2)={n!_(gamma)_n}L_n^(gamma-1)(x^2), appear in the
first-order perturbation correction for the wavefunction of the generalized
spiked harmonic oscillator Hamiltonian H = -d^2/dx^2 + B x^2 + A/x^2 +
lambda/x^alpha 0 0, A >= 0. It is proved that the
series is convergent for all x > 0 and 2 gamma > alpha, where gamma = 1 +
(1/2)sqrt(1+4A). Closed-form sums are presented for these series for the cases
alpha = 2, 4, and 6. A general formula for finding the sum for alpha/2 = 2 + m,
m = 0,1,2, ..., in terms of associated Laguerre polynomials, is also provided.Comment: 16 page
Are Americans confident their ballots are counted?
Building on the literature that investigates citizen and voter trust in government, we analyze the topic of voter confidence in the American electoral process. Our data comes from two national telephone surveys where voters were asked the confidence they have that their vote for president in the 2004 election was recorded as intended. We present preliminary evidence that suggests confidence in the electoral process affects voter turnout. We then examine voter responses to determine the overall level of voter confidence and analyze the characteristics that influence the likelihood a voter is confident that their ballot was recorded accurately. Our analyses indicate significant differences in the level of voter confidence along both racial and partisan lines. Finally, we find voter familiarity with the electoral process, opinions about the electoral process in other voting precincts, and both general opinions about voting technology and the specific technology the voter uses significantly affect the level of voter confidence
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