2,700 research outputs found
The space of solutions to the Hessian one equation in the finitely punctured plane
We construct the space of solutions to the elliptic Monge-Ampere equation
det(D^2 u)=1 in the plane R^2 with n points removed. We show that, modulo
equiaffine transformations and for n>1, this space can be seen as an open
subset of R^{3n-4}, where the coordinates are described by the conformal
equivalence classes of once punctured bounded domains in the complex plane of
connectivity n-1. This approach actually provides a constructive procedure that
recovers all such solutions to the Monge-Ampere equation, and generalizes a
theorem by K. Jorgens.Comment: 14 pages, 3 figure
Excited states of beryllium atom from explicitly correlated wave functions
A study of the first excited states of beryllium atom starting from
explicitly correlated wave functions is carried out. Several properties are
obtained and discussed focusing on the analysis of the Hund's rules in terms of
the single--particle and electron pair intracule and extracule densities. A
systematic study of the differences on the electronic distributions of the
singlet and triplet states is carried out. The trial wave function used to
describe the different bound states consists of a generalized Jastrow-type
correlation factor times a configuration interaction model wave function. This
model wave function has been fixed by using a generalization of the optimized
effective potential method to deal with multiconfiguration wave functions. The
optimization of the wave function and the calculation of the different
quantities is carried out by means of the Variational Monte Carlo method.Comment: 28 pages, 6 figure
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