1,845 research outputs found
Asymptotic iteration method for eigenvalue problems
An asymptotic interation method for solving second-order homogeneous linear
differential equations of the form y'' = lambda(x) y' + s(x) y is introduced,
where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to
Schroedinger type problems, including some with highly singular potentials, are
presented.Comment: 14 page
Perturbation expansions for a class of singular potentials
Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is
applied and extended to obtain non-power perturbation expansions for a class of
singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha
> 2), known as generalized spiked harmonic oscillators. The perturbation
expansions developed here are valid for small values of the coupling lambda >
0, and they extend the results which Harrell obtained for the spiked harmonic
oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page
Variational analysis for a generalized spiked harmonic oscillator
A variational analysis is presented for the generalized spiked harmonic
oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 +
lambda/x^alpha, and alpha and lambda are real positive parameters. The
formalism makes use of a basis provided by exact solutions of Schroedinger's
equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the
corresponding matrix elements that were previously found. For all the discrete
eigenvalues the method provides bounds which improve as the dimension of the
basis set is increased. Extension to the N-dimensional case in arbitrary
angular-momentum subspaces is also presented. By minimizing over the free
parameter A, we are able to reduce substantially the number of basis functions
needed for a given accuracy.Comment: 15 pages, 1 figur
Bender-Wu Formula and the Stark Effect in Hydrogen
We discuss a close connection between the formula of Banks, Bender, and Wu for the asymptotics of the Rayleigh-Schrödinger coefficients of the two-dimensional rotationally symmetric anharmonic oscillator and the behavior of resonances of the hydrogen Stark problem in two regimes: small field (Oppenheimer's formula) and large field (where we obtain the new results arg E → −π/3, ∣E∣ ∼α[F(lnF)^(2/3) for F, the electric field strength, going to infinity). We also announce a rigorous proof of Bender-Wu-type formulas
Part of the D - dimensional Spiked harmonic oscillator spectra
The pseudoperturbative shifted - l expansion technique PSLET [5,20] is
generalized for states with arbitrary number of nodal zeros. Interdimensional
degeneracies, emerging from the isomorphism between angular momentum and
dimensionality of the central force Schrodinger equation, are used to construct
part of the D - dimensional spiked harmonic oscillator bound - states. PSLET
results are found to compare excellenly with those from direct numerical
integration and generalized variational methods [1,2].Comment: Latex file, 20 pages, to appear in J. Phys. A: Math. & Ge
Resonances Width in Crossed Electric and Magnetic Fields
We study the spectral properties of a charged particle confined to a
two-dimensional plane and submitted to homogeneous magnetic and electric fields
and an impurity potential. We use the method of complex translations to prove
that the life-times of resonances induced by the presence of electric field are
at least Gaussian long as the electric field tends to zero.Comment: 3 figure
Synthesis and magnetic properties of CoPt nanoparticles
High magnetocrystalline anisotropy CoPt particles with an average size of 8 nm were synthesized by the superhydride reduction of CoCl2CoCl2 and Pt(acac)2Pt(acac)2 at a high temperature. As-made particles showed a disordered face-centered cubic lattice and were superparamagnetic. Upon heat treatment at temperatures above 600 °C, the particles transformed to the L10L10 phase, as indicated by the appearance of the superlattice peaks in the x-ray diffraction and high magnetocrystalline anisotropy. The temperature dependence of the coercivity of nanoparticles annealed at 650 °C was measured from 10 to 300 K and analyzed using a Sharrock formula. After annealing at 650 °C, the anisotropy of the nanoparticles was K∼1.7×107 erg/cm3.K∼1.7×107 erg/cm3. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69714/2/JAPIAU-95-11-6747-1.pd
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