65,645 research outputs found
Pseudospectral Calculation of the Wavefunction of Helium and the Negative Hydrogen Ion
We study the numerical solution of the non-relativistic Schr\"{o}dinger
equation for two-electron atoms in ground and excited S-states using
pseudospectral (PS) methods of calculation. The calculation achieves
convergence rates for the energy, Cauchy error in the wavefunction, and
variance in local energy that are exponentially fast for all practical
purposes. The method requires three separate subdomains to handle the
wavefunction's cusp-like behavior near the two-particle coalescences. The use
of three subdomains is essential to maintaining exponential convergence. A
comparison of several different treatments of the cusps and the semi-infinite
domain suggest that the simplest prescription is sufficient. For many purposes
it proves unnecessary to handle the logarithmic behavior near the
three-particle coalescence in a special way. The PS method has many virtues: no
explicit assumptions need be made about the asymptotic behavior of the
wavefunction near cusps or at large distances, the local energy is exactly
equal to the calculated global energy at all collocation points, local errors
go down everywhere with increasing resolution, the effective basis using
Chebyshev polynomials is complete and simple, and the method is easily
extensible to other bound states. This study serves as a proof-of-principle of
the method for more general two- and possibly three-electron applications.Comment: 23 pages, 20 figures, 2 tables, Final refereed version - Some
references added, some stylistic changes, added paragraph to matrix methods
section, added last sentence to abstract
Improving Sensitivity to Weak Pulsations with Photon Probability Weighting
All gamma-ray telescopes suffer from source confusion due to their inability
to focus incident high-energy radiation, and the resulting background
contamination can obscure the periodic emission from faint pulsars. In the
context of the Fermi Large Area Telescope, we outline enhanced statistical
tests for pulsation in which each photon is weighted by its probability to have
originated from the candidate pulsar. The probabilities are calculated using
the instrument response function and a full spectral model, enabling powerful
background rejection. With Monte Carlo methods, we demonstrate that the new
tests increase the sensitivity to pulsars by more than 50% under a wide range
of conditions. This improvement may appreciably increase the completeness of
the sample of radio-loud gamma-ray pulsars. Finally, we derive the asymptotic
null distribution for the H-test, expanding its domain of validity to
arbitrarily complex light curves.Comment: 10 pages, 11 figures, published by ApJ; v2 fixes an error in Eq.
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