60,254 research outputs found
Relativistic N-boson systems bound by pair potentials V(r_{ij}) = g(r_{ij}^2)
We study the lowest energy E of a relativistic system of N identical bosons
bound by pair potentials of the form V(r_{ij}) = g(r_{ij}^2) in three spatial
dimensions. In natural units hbar = c = 1 the system has the semirelativistic
`spinless-Salpeter' Hamiltonian H = \sum_{i=1}^N \sqrt{m^2 + p_i^2} +
\sum_{j>i=1}^N g(|r_i - r_j|^2), where g is monotone increasing and has
convexity g'' >= 0. We use `envelope theory' to derive formulas for general
lower energy bounds and we use a variational method to find complementary upper
bounds valid for all N >= 2. In particular, we determine the energy of the
N-body oscillator g(r^2) = c r^2 with error less than 0.15% for all m >= 0, N
>= 2, and c > 0.Comment: 15 pages, 4 figure
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
Convexity and potential sums for Salpeter-like Hamiltonians
The semirelativistic Hamiltonian H = \beta\sqrt{m^2 + p^2} + V(r), where V(r)
is a central potential in R^3, is concave in p^2 and convex in p. This fact
enables us to obtain complementary energy bounds for the discrete spectrum of
H. By extending the notion of 'kinetic potential' we are able to find general
energy bounds on the ground-state energy E corresponding to potentials with the
form V = sum_{i}a_{i}f^{(i)}(r). In the case of sums of powers and the log
potential, where V(r) = sum_{q\ne 0} a(q) sgn(q)r^q + a(0)ln(r), the bounds can
all be expressed in the semi-classical form E \approx \min_{r}{\beta\sqrt{m^2 +
1/r^2} + sum_{q\ne 0} a(q)sgn(q)(rP(q))^q + a(0)ln(rP(0))}. 'Upper' and 'lower'
P-numbers are provided for q = -1,1,2, and for the log potential q = 0. Some
specific examples are discussed, to show the quality of the bounds.Comment: 21 pages, 4 figure
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
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
Misregistration's effects on classification and proportion estimation accuracy
The estimates of crop type and acreage are undertaken in the AgRISTARS program by registering multiple date acquisitions of small subareas of LANDSAT scenes (termed segments), and applying multispectral analysis to them. An important contribution to errors in classification and acreage estimates is misregistration between multiple acquisitions. The formula used to express this relationship is given and the operations applied are so shown in diagrams. The taking of a LANDSAT feature vector and the derivation of the brightness and greeness are illustrated. It is shown that for any given sensor IFOV geometry, typical populations of fields can be derived and histograms can be plotted of the number of fields against field size according to ground truth. As a function of the resolution element, the IFOV of the sensor can draw the proportion of pure pixels in a given crop. Because the thematic mapper has a smaller resolution, the proportion of pixels that are pure in any given area will be larger
Application of satellite imagery to hydrologic modeling snowmelt runoff in the southern Sierra Nevada
There are no author-identified significant results in this report
The large area crop inventory experiment: A major demonstration of space remote sensing
Strategies are presented in agricultural technology to increase the resistance of crops to a wider range of meteorological conditions in order to reduce year-to-year variations in crop production. Uncertainties in agricultral production, together with the consumer demands of an increasing world population, have greatly intensified the need for early and accurate annual global crop production forecasts. These forecasts must predict fluctuation with an accuracy, timeliness and known reliability sufficient to permit necessary social and economic adjustments, with as much advance warning as possible
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
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
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