3,887 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
Duality relations in the auxiliary field method
The eigenenergies of a system of
identical particles with a mass are functions of the various radial quantum
numbers and orbital quantum numbers . Approximations
of these eigenenergies, depending on a principal quantum number
, can be obtained in the framework of the auxiliary field
method. We demonstrate the existence of numerous exact duality relations
linking quantities and for various forms of the
potentials (independent of and ) and for both nonrelativistic and
semirelativistic kinematics. As the approximations computed with the auxiliary
field method can be very close to the exact results, we show with several
examples that these duality relations still hold, with sometimes a good
accuracy, for the exact eigenenergies
CVD of CrO2 Thin Films: Influence of the Deposition Parameters on their Structural and Magnetic Properties
This work reports on the synthesis of CrO2 thin films by atmospheric pressure
CVD using chromium trioxide (CrO3) and oxygen. Highly oriented (100) CrO2 films
containing highly oriented (0001) Cr2O3 were grown onto Al2O3(0001) substrates.
Films display a sharp magnetic transition at 375 K and a saturation
magnetization of 1.92 Bohr magnetons per f.u., close to the bulk value of 2
Bohr magnetons per f.u. for the CrO2.
Keywords: Chromium dioxide (CrO2), Atmospheric pressure CVD, Spintronics.Comment: 5 pages, 6 figure
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
Full-vector analysis of a realistic photonic crystal fiber
We analyze the guiding problem in a realistic photonic crystal fiber using a
novel full-vector modal technique, a biorthogonal modal method based on the
nonselfadjoint character of the electromagnetic propagation in a fiber.
Dispersion curves of guided modes for different fiber structural parameters are
calculated along with the 2D transverse intensity distribution of the
fundamental mode. Our results match those achieved in recent experiments, where
the feasibility of this type of fiber was shown.Comment: 3 figures, submitted to Optics Letter
Synthesis and properties of Co-doped titanate nanotubes and their optical sensitization with methylene blue
Here we report on a novel chemical route to synthesize homogenous cobalt
doped titanate nanotubes (CoTNT), using an amorphous Co-doped precursor. The
influence of the synthesis temperature, autoclave dwell time and metal doping
on the structural and microstructural as well as on the optical properties of
the synthesized titanate nanotubes is studied and discussed. The optical band
gaps of the CoTNT samples are red shifted in comparison with the values
determined for the undoped samples, such red shifts bringing the absorption
edge of the CoTNT samples into the visible region. CoTNT materials also
demonstrate particular high adsorption ability for methylene blue, the amount
of the adsorbed dye being higher than the one predictable for a monolayer
formation. This suggests the possibility of intercalation of the dye molecule
between the TiO6 layers of the TNT structure. It is also shown that the
methylene blue sensitized Co-doped nanostructures are highly stable under UV
radiation and present a strong and broad absorption in the visible region.Comment: 31 pages, 3 tables, 7 figure
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