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

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 $|t|^{1- alpha}$ singularity that sets in sharply for $|t|\equiv |T-T_c|/T_c\lesssim 10^{-3}$; this compares favorably with extensive data for ${SF}_6$, also reflec ted in C$_2$H$_6$, N$_2$, etc. By contrast, the curvature of the RPM diameter va ries slowly over a wide range $|t|\lesssim 0.1$; 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

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

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

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.

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

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

Full capacitance-matrix effects in driven Josephson-junction arrays

We study the dynamic response to external currents of periodic arrays of Josephson junctions, in a resistively capacitively shunted junction (RCSJ) model, including full capacitance-matrix effects}. We define and study three different models of the capacitance matrix $C_{\vec{r},\vec{r}'}$: Model A includes only mutual capacitances; Model B includes mutual and self capacitances, leading to exponential screening of the electrostatic fields; Model C includes a dense matrix $C_{\vec{r},\vec{r}'}$ that is constructed approximately from superposition of an exact analytic solution for the capacitance between two disks of finite radius and thickness. In the latter case the electrostatic fields decay algebraically. For comparison, we have also evaluated the full capacitance matrix using the MIT fastcap algorithm, good for small lattices, as well as a corresponding continuum effective-medium analytic evaluation of a finite voltage disk inside a zero-potential plane. In all cases the effective $C_{\vec{r},\vec{r}'}$ decays algebraically with distance, with different powers. We have then calculated current voltage characteristics for DC+AC currents for all models. We find that there are novel giant capacitive fractional steps in the I-V's for Models B and C, strongly dependent on the amount of screening involved. We find that these fractional steps are quantized in units inversely proportional to the lattice sizes and depend on the properties of $C_{\vec{r},\vec{r}'}$. We also show that the capacitive steps are not related to vortex oscillations but to localized screened phase-locking of a few rows in the lattice. The possible experimental relevance of these results is also discussed.Comment: 12 pages 18 Postscript figures, REVTEX style. Paper to appear in July 1, Vol. 58, Phys. Rev. B 1998 All PS figures include

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 $^{7}Li_{2}$ 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