79,442 research outputs found
Functional inversion for potentials in quantum mechanics
Let E = F(v) be the ground-state eigenvalue of the Schroedinger Hamiltonian H
= -Delta + vf(x), where the potential shape f(x) is symmetric and monotone
increasing for x > 0, and the coupling parameter v is positive.
If the 'kinetic potential' bar{f}(s) associated with f(x) is defined by the
transformation: bar{f}(s) = F'(v), s = F(v)-vF'(v),then f can be reconstructed
from F by the sequence: f^{[n+1]} = bar{f} o bar{f}^{[n]^{-1}} o f^{[n]}.
Convergence is proved for special classes of potential shape; for other test
cases it is demonstrated numerically. The seed potential shape f^{[0]} need not
be 'close' to the limit f.Comment: 14 pages, 2 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
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
Asymptotic analysis of a pile-up of edge dislocation
The idealised problem of a pile-up of dislocation walls (that is, of planes each containing an infinite number of parallel and identical dislocations) was presented by Roy et al. (Mater. Sci. Eng. A 486:653-661, 2008) as a proto-type for understanding the importance of discrete dislocation interactions in dislocation-based plasticity models. They noted that analytic solutions for the dislocation wall density are available for a pile-up of screw dislocation walls, but that numerical methods seem to be necessary for investigating edge dislocation walls. In this paper, we use the techniques of discrete-to-continuum asymptotic analysis to obtain a detailed description of a pile-up of edge dislocation walls. To leading order, we find that the dislocation wall density is governed by a simple differential equation and that boundary layers are present at both ends of the pile-up
Non-profit Health Care Services Marketing: Persuasive Messages Based on Multidimensional Concept Mapping and Direct Magnitude Estimation
Persuasive messages for marketing healthcare services in general and coordinated care in particular are more important now for providers, hospitals, and third-party payers than ever before. The combination of measurement based information with creativity may be among the most critical factors in reaching markets or expanding markets. The research presented here provides an approach to marketing coordinated care services which allows healthcare managers to plan persuasive messages given the market conditions they face. Using market respondents’ thinking about product attributes combined with distance measurement between pairs of product attributes, a conceptual marketing map is presented and applied to advertising, message copy, and delivery. The data reported here are representative of the potential caregivers for which the messages are intended. Results are described with implications for application to coordinated care services. Theory building and marketing practice are discussed in the light of findings and methodology
Spectral bounds for the cutoff Coulomb potential
The method of potential envelopes is used to analyse the bound-state spectrum
of the Schroedinger Hamiltonian H = -Delta -v/(r+b), where v and b are
positive. We established simple formulas yielding upper and lower energy bounds
for all the energy eigenvalues.Comment: 11 pages, 2 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
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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