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 $V(\rho,\rho_0)=\mu\omega^2|\rho^2-\rho_0^2|/2$.Comment: 10 pages, LaTex, 6 figures (eps). accepted in Phys. Lett.

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

Superintegrability on the two dimensional hyperboloid II

This work is devoted to the investigation of the quantum mechanical systems on the two dimensional hyperboloid which admit separation of variables in at least two coordinate systems. Here we consider two potentials introduced in a paper of C.P.Boyer, E.G.Kalnins and P.Winternitz, which haven't yet been studied. We give an example of an interbasis expansion and work out the structure of the quadratic algebra generated by the integrals of motion.Comment: 18 pages, LaTex; 1 figure (eps

Quantum oscillator as 1D anyon

It is shown that in one spatial dimension the quantum oscillator is dual to the charged particle situated in the field described by the superposition of Coulomb and Calogero-Sutherland potentials.Comment: 9 pages, LaTe

Target and beam-target spin asymmetries in exclusive pion electroproduction for Q2>1GeV2 . I. ep→eπ+n

Beam-target double-spin asymmetries and target single-spin asymmetries were measured for the exclusive π + electroproduction reaction γ ∗ p → n π + . The results were obtained from scattering of 6-GeV longitudinally polarized electrons off longitudinally polarized protons using the CEBAF Large Acceptance Spectrometer at Jefferson Laboratory. The kinematic range covered is 1.1 < W < 3 GeV and 1 < Q 2 < 6 GeV 2 . Results were obtained for about 6000 bins in W ,   Q 2 ,   cos ( θ ∗ ) , and ϕ ∗ . Except at forward angles, very large target-spin asymmetries are observed over the entire W region. Reasonable agreement is found with phenomenological fits to previous data for W < 1.6 GeV, but very large differences are seen at higher values of W . A generalized parton distributions (GPD)-based model is in poor agreement with the data. When combined with cross-sectional measurements, the present results provide powerful constraints on nucleon resonance amplitudes at moderate and large values of Q 2 , for resonances with masses as high as 2.4 GeV

Demonstration of a novel technique to measure two-photon exchange effects in elastic e±pe^\pm p scattering

The discrepancy between proton electromagnetic form factors extracted using unpolarized and polarized scattering data is believed to be a consequence of two-photon exchange (TPE) effects. However, the calculations of TPE corrections have significant model dependence, and there is limited direct experimental evidence for such corrections. We present the results of a new experimental technique for making direct $e^\pm p$ comparisons, which has the potential to make precise measurements over a broad range in $Q^2$ and scattering angles. We use the Jefferson Lab electron beam and the Hall B photon tagger to generate a clean but untagged photon beam. The photon beam impinges on a converter foil to generate a mixed beam of electrons, positrons, and photons. A chicane is used to separate and recombine the electron and positron beams while the photon beam is stopped by a photon blocker. This provides a combined electron and positron beam, with energies from 0.5 to 3.2 GeV, which impinges on a liquid hydrogen target. The large acceptance CLAS detector is used to identify and reconstruct elastic scattering events, determining both the initial lepton energy and the sign of the scattered lepton. The data were collected in two days with a primary electron beam energy of only 3.3 GeV, limiting the data from this run to smaller values of $Q^2$ and scattering angle. Nonetheless, this measurement yields a data sample for $e^\pm p$ with statistics comparable to those of the best previous measurements. We have shown that we can cleanly identify elastic scattering events and correct for the difference in acceptance for electron and positron scattering. The final ratio of positron to electron scattering: $R=1.027\pm0.005\pm0.05$ for $=0.206$ GeV$^2$ and $0.830\leq \epsilon\leq 0.943$