2,314 research outputs found
Distributional Borel Summability of Odd Anharmonic Oscillators
It is proved that the divergent Rayleigh-Schrodinger perturbation expansions
for the eigenvalues of any odd anharmonic oscillator are Borel summable in the
distributional sense to the resonances naturally associated with the system
Faraday effect revisited: sum rules and convergence issues
This is the third paper of a series revisiting the Faraday effect. The
question of the absolute convergence of the sums over the band indices entering
the Verdet constant is considered. In general, sum rules and traces per unit
volume play an important role in solid state physics, and they give rise to
certain convergence problems widely ignored by physicists. We give a complete
answer in the case of smooth potentials and formulate an open problem related
to less regular perturbations.Comment: Dedicated to the memory of our late friend Pierre Duclos. Accepted
for publication in Journal of Physics A: Mathematical and Theoretical
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
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
Ellipsometric study of Si(0.5)Ge(0.5)/Si strained-layer superlattices
An ellipsometric study of two Si(0.5)Ge(0.5)/Si strained-layer super lattices grown by MBE at low temperature (500 C) is presented, and results are compared with x ray diffraction (XRD) estimates. Excellent agreement is obtained between target values, XRD, and ellipsometry when one of two available Si(x)Ge(1-x) databases is used. It is shown that ellipsometry can be used to nondestructively determine the number of superlattice periods, layer thicknesses, Si(x)Ge(1-x) composition, and oxide thickness without resorting to additional sources of information. It was also noted that we do not observe any strain effect on the E(sub 1) critical point
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
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