209 research outputs found
Ladder Operators for Quantum Systems Confined by Dihedral Angles
We report the identification and construction of raising and lowering
operators for the complete eigenfunctions of isotropic harmonic oscillators
confined by dihedral angles, in circular cylindrical and spherical coordinates;
as well as for the hydrogen atom in the same situation of confinement, in
spherical, parabolic and prolate spheroidal coordinates. The actions of such
operators on any eigenfunction are examined in the respective coordinates,
illustrating the possibility of generating the complete bases of eigenfunctions
in the respective coordinates for both physical systems. The relationships
between the eigenfunctions in each pair of coordinates, and with the same
eigenenergies are also illustrated
Magnetic induction ¯elds and potentials from electrical currents on elliptical cylinders
Indução magnética de campos e potenciais produzidos por correntes elétricas ao longo de um cilindro elíptico infinito e ao longo de um solenóide cilíndrico infinitamente longo, respectivamente, são calculados explicitamente. As similaridades e as diferenças das distribuições de correntes, campos de indução magnética e potenciais desses sistemas eletromagnéticos são comparados com os dos cilindros correspondentes com secções circulares
Free-particle and harmonic-oscillator propagators in two and three dimensions
This contribution illustrates how to construct free-particle and harmonic-oscillator quantum-mechanical propagators in two and three dimensions in cartesian, and in circular and spherical coordinates, respectively, starting from the corresponding one-dimensional propagators in cartesian coordinates
Connection Between Type A and E Factorizations and Construction of Satellite Algebras
Recently, we introduced a new class of symmetry algebras, called satellite
algebras, which connect with one another wavefunctions belonging to different
potentials of a given family, and corresponding to different energy
eigenvalues. Here the role of the factorization method in the construction of
such algebras is investigated. A general procedure for determining an so(2,2)
or so(2,1) satellite algebra for all the Hamiltonians that admit a type E
factorization is proposed. Such a procedure is based on the known relationship
between type A and E factorizations, combined with an algebraization similar to
that used in the construction of potential algebras. It is illustrated with the
examples of the generalized Morse potential, the Rosen-Morse potential, the
Kepler problem in a space of constant negative curvature, and, in each case,
the conserved quantity is identified. It should be stressed that the method
proposed is fairly general since the other factorization types may be
considered as limiting cases of type A or E factorizations.Comment: 20 pages, LaTeX, no figure, to be published in J. Phys.
Ground state study of simple atoms within a nano-scale box
Ground state energies for confined hydrogen (H) and helium (He) atoms, inside
a penetrable/impenetrable compartment have been calculated using Diffusion
Monte Carlo (DMC) method. Specifically, we have investigated spherical and
ellipsoidal encompassing compartments of a few nanometer size. The potential is
held fixed at a constant value on the surface of the compartment and beyond.
The dependence of ground state energy on the geometrical characteristics of the
compartment as well as the potential value on its surface has been thoroughly
explored. In addition, we have investigated the cases where the nucleus
location is off the geometrical centre of the compartment.Comment: 9 pages, 5 eps figures, Revte
Singular Coexistence-curve Diameters: Experiments and Simulations
Precise calculations of the coexistence-curve diameters of a hard-core
square-we ll (HCSW) fluid and the restricted primitive model (RPM) electrolyte
exhibit mar ked deviations from rectilinear behavior. The HCSW diameter
displays a singularity that sets in sharply for ; this compares favorably with extensive data for
, also reflec ted in CH, N, etc. By contrast, the curvature
of the RPM diameter va ries slowly over a wide range ; this
behavior mirrors observati ons for liquid alkali metals, specifically Rb and
Cs. Amplitudes for the leading singular terms can be estimated numerically but
their values cannot be taken li terally.Comment: 9 pages and 4 figure
Stark effect in a wedge-shaped quantum box
The effect of an external applied electric field on the electronic ground
state energy of a quantum box with a geometry defined by a wedge is studied by
carrying out a variational calculation. This geometry could be used as an
approximation for a tip of a cantilever of an atomic force microscope. We study
theoretically the Stark effect as function of the parameters of the wedge: its
diameter, angular aperture and thickness; as well as function of the intensity
of the external electric field applied along the axis of the wedge in both
directions; pushing the carrier towards the wider or the narrower parts. A
confining electronic effect, which is sharper as the wedge dimensions are
smaller, is clearly observed for the first case. Besides, the sign of the Stark
shift changes when the angular aperture is changed from small angles to angles
theta>pi. For the opposite field, the electronic confinement for large
diameters is very small and it is also observed that the Stark shift is almost
independent with respect to the angular aperture.Comment: 23 pages, 9 figures, 1 tabl
On a Generalized Kepler-Coulomb System: Interbasis Expansions
This paper deals with a dynamical system that generalizes the Kepler-Coulomb
system and the Hartmann system. It is shown that the Schr\"odinger equation for
this generalized Kepler-Coulomb system can be separated in prolate spheroidal
coordinates. The coefficients of the interbasis expansions between three bases
(spherical, parabolic and spheroidal) are studied in detail. It is found that
the coefficients for the expansion of the parabolic basis in terms of the
spherical basis, and vice-versa, can be expressed through the Clebsch-Gordan
coefficients for the group SU(2) analytically continued to real values of their
arguments. The coefficients for the expansions of the spheroidal basis in terms
of the spherical and parabolic bases are proved to satisfy three-term recursion
relations.Comment: 24 pages, Latex, LYCEN 941
Exact solutions for vibrational levels of the Morse potential via the asymptotic iteration method
Exact solutions for vibrational levels of diatomic molecules via the Morse
potential are obtained by means of the asymptotic iteration method. It is shown
that, the numerical results for the energy eigenvalues of are all
in excellent agreement with the ones obtained before. Without any loss of
generality, other states and molecules could be treated in a similar way
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