4,274 research outputs found
Auxiliary field method and analytical solutions of the Schr\"{o}dinger equation with exponential potentials
The auxiliary field method is a new and efficient way to compute approximate
analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This
method has already been successfully applied to the case of central potentials
of power-law and logarithmic forms. In the present work, we show that the
Schr\"{o}dinger equation with exponential potentials of the form can also be analytically solved by using the
auxiliary field method. Formulae giving the critical heights and the energy
levels of these potentials are presented. Special attention is drawn on the
Yukawa potential and the pure exponential one
Extensions of the auxiliary field method to solve Schr\"{o}dinger equations
It has recently been shown that the auxiliary field method is an interesting
tool to compute approximate analytical solutions of the Schr\"{o}dinger
equation. This technique can generate the spectrum associated with an arbitrary
potential starting from the analytically known spectrum of a particular
potential . In the present work, general important properties of the
auxiliary field method are proved, such as scaling laws and independence of the
results on the choice of . The method is extended in order to find
accurate analytical energy formulae for radial potentials of the form , and several explicit examples are studied. Connections existing
between the perturbation theory and the auxiliary field method are also
discussed
Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer
Grand canonical Monte Carlo simulation results are reported for an electric
double layer modelled by a planar charged hard wall, anisotropic shape cations,
and spherical anions at different electrolyte concentrations and asymmetric
valencies. The cations consist of two tangentially tethered hard spheres of the
same diameter, . One sphere is charged while the other is neutral. Spherical
anions are charged hard spheres of diameter . The ion valency asymmetry 1:2
and 2:1 is considered, with the ions being immersed in a solvent mimicked by a
continuum dielectric medium at standard temperature. The simulations are
carried out for the following electrolyte concentrations: 0.1, 1.0 and 2.0 M.
Profiles of the electrode-ion, electrode-neutral sphere singlet distributions,
the average orientation of dimers, and the mean electrostatic potential are
calculated for a given electrode surface charge, , while the contact
electrode potential and the differential capacitance are presented for varying
electrode charge. With an increasing electrolyte concentration, the shape of
differential capacitance curve changes from that with a minimum surrounded by
maxima into that of a distorted single maximum. For a 2:1 electrolyte, the
maximum is located at a small negative value while for 1:2, at a small
positive value.Comment: 10 pages, 6 figure
Double layer for hard spheres with an off-center charge
Simulations for the density and potential profiles of the ions in the planar
electrical double layer of a model electrolyte or an ionic liquid are reported.
The ions of a real electrolyte or an ionic liquid are usually not spheres; in
ionic liquids, the cations are molecular ions. In the past, this asymmetry has
been modelled by considering spheres that are asymmetric in size and/or valence
(viz., the primitive model) or by dimer cations that are formed by tangentially
touching spheres. In this paper we consider spherical ions that are asymmetric
in size and mimic the asymmetrical shape through an off-center charge that is
located away from the center of the cation spheres, while the anion charge is
at the center of anion spheres. The various singlet density and potential
profiles are compared to (i) the dimer situation, that is, the constituent
spheres of the dimer cation are tangentially tethered, and (ii) the standard
primitive model. The results reveal the double layer structure to be
substantially impacted especially when the cation is the counterion. As well as
being of intrinsic interest, this off-center charge model may be useful for
theories that consider spherical models and introduce the off-center charge as
a perturbation.Comment: 11 pages, 7 figure
A (p/E) Calculation of Strong Pionic Decays of Baryons
Strong pionic decays of baryons are studied in a non-relativistic quark model
framework via a convergent (p/E) expansion of the transition operator. Results
are compared to the ones obtained within a more conventional (p/m) expansion.Comment: 16 pages, LaTeX, using amssymb.st
The few-body problem in terms of correlated gaussians
In their textbook, Suzuki and Varga [Y. Suzuki and K. Varga, {\em Stochastic
Variational Approach to Quantum-Mechanical Few-Body Problems} (Springer,
Berlin, 1998)] present the stochastic variational method in a very exhaustive
way. In this framework, the so-called correlated gaussian bases are often
employed. General formulae for the matrix elements of various operators can be
found in the textbook. However the Fourier transform of correlated gaussians
and their application to the management of a relativistic kinetic energy
operator are missing and cannot be found in the literature. In this paper we
present these interesting formulae. We give also a derivation for new
formulations concerning central potentials; the corresponding formulae are more
efficient numerically than those presented in the textbook.Comment: 10 page
Semirelativistic Hamiltonians and the auxiliary field method
Approximate analytical closed energy formulas for semirelativistic
Hamiltonians of the form are obtained within
the framework of the auxiliary field method. This method, which is equivalent
to the envelope theory, has been recently proposed as a powerful tool to get
approximate analytical solutions of the Schr\"odinger equation. Various shapes
for the potential are investigated: power-law, funnel, square root, and
Yukawa. A comparison with the exact results is discussed in detail
Synthesis of sub-5 nm Co-doped SnO nanoparticles and their structural, microstructural, optical and photocatalytic properties
A swift chemical route to synthesize Co-doped SnO nanopowders is
described. Pure and highly stable SnCoO (0 x
0.15) crystalline nanoparticles were synthesized, with mean grain sizes <
5 nm and the dopant element homogeneously distributed in substitutional sites
of the SnO matrix. The UV-visible diffuse reflectance spectra of the
SnCoO samples reveal red shifts, the optical bandgap
energies decreasing with increasing Co concentration. The Urbach energies of
the samples were calculated and correlated with their bandgap energies. The
photocatalytic activity of the SnCoO samples was
investigated for the 4-hydroxylbenzoic acid (4-HBA) degradation process. A
complete photodegradation of a 10 ppm 4-HBA solution was achieved using 0.02%
(w/w) of SnCoO nanoparticles in 60 min of
irradiation.Comment: 29 pages, 2 tables, 10 figure
Argon assisted chemical vapor deposition of CrO: an efficient process leading to high quality epitaxial films
A comparative study of the structural, microstructural and magnetic
properties of CrO thin films grown onto (110) and (100) TiO rutile
single crystal substrates by chemical vapor deposition (CVD), using CrO as
chromium precursor and either oxygen or argon as carrier gas is presented. Our
results show that growth under argon carrier gas leads to high quality CrO
epilayers with structural and magnetic properties similar to those obtained
using the more standard oxygen carrier gas. Furthermore, we interpret the
larger magnetic coercivity observed for the (110) oriented films in terms of
their microstructure, in particular of the highest strain and edge roughness of
the building structures of the CrO epilayers, which are settled by the
substrate crystallographic orientation.Comment: 27 pages, 2 tables, 8 figure
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