2,318 research outputs found
Lattice electrons in constant magnetic field: Bethe like ansatz
We use the functional representation of Heisenberg-Weyl group and obtain
equation for the spectrum of the model, which is more complicated than Bethes
ones, but can be written explicitly through theta functions.Comment: 8 pages, LATE
Quantum Parabolic Sombrero
We have discussed the energy levels and probability distribution density for
a quantum particle placed in the two-dimensional sombrero-shaped potential
.Comment: 10 pages, LaTex, 6 figures (eps). accepted in Phys. Lett.
On a Generalized Oscillator: Invariance Algebra and Interbasis Expansions
This article deals with a quantum-mechanical system which generalizes the
ordinary isotropic harmonic oscillator system. We give the coefficients
connecting the polar and Cartesian bases for D=2 and the coefficients
connecting the Cartesian and cylindrical bases as well as the cylindrical and
spherical bases for D=3. These interbasis expansion coefficients are found to
be analytic continuations to real values of their arguments of the
Clebsch-Gordan coefficients for the group SU(2). For D=2, the superintegrable
character for the generalized oscillator system is investigated from the points
of view of a quadratic invariance algebra.Comment: 13 pages, Latex file. Submitted for publication to Yadernaya Fizik
Searching for solar siblings among the HARPS data
The search for the solar siblings has been particularly fruitful in the last
few years. Until now, there are four plausible candidates pointed out in the
literature: HIP21158, HIP87382, HIP47399, and HIP92831. In this study we
conduct a search for solar siblings among the HARPS high-resolution FGK dwarfs
sample, which includes precise chemical abundances and kinematics for 1111
stars. Using a new approach based on chemical abundance trends with the
condensation temperature, kinematics, and ages we found one (additional)
potential solar sibling candidate: HIP97507.Comment: 4 pages, 2 figures, 1 table. Accepted in A&
Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries
We show that second-order superintegrable systems in two-dimensional and three-dimensional Euclidean space generate both exactly solvable (ES) and quasiexactly solvable (QES) problems in quantum mechanics via separation of variables, and demonstrate the increased insight into the structure of such problems provided by superintegrability. A principal advantage of our analysis using nondegenerate superintegrable systems is that they are multiseparable. Most past separation of variables treatments of QES problems via partial differential equations have only incorporated separability, not multiseparability. Also, we propose another definition of ES and QES. The quantum mechanical problem is called ES if the solution of Schrödinger equation can be expressed in terms of hypergeometric functions mFn and is QES if the Schrödinger equation admits polynomial solutions with coefficients necessarily satisfying a three-term or higher order of recurrence relations. In three dimensions we give an example of a system that is QES in one set of separable coordinates, but is not ES in any other separable coordinates. This example encompasses Ushveridze's tenth-order polynomial QES problem in one set of separable coordinates and also leads to a fourth-order polynomial QES problem in another separable coordinate set
- …