On Exactness Of The Supersymmetric WKB Approximation Scheme

Exactness of the lowest order supersymmetric WKB (SWKB) quantization condition $\int^{x_2}_{x_1} \sqrt{E-\omega^2(x)} dx = n \hbar \pi$, for certain potentials, is examined, using complex integration technique. Comparison of the above scheme with a similar, but {\it exact} quantization condition, $\oint_c p(x,E) dx = 2\pi n \hbar$, originating from the quantum Hamilton-Jacobi formalism reveals that, the locations and the residues of the poles that contribute to these integrals match identically, for both of these cases. As these poles completely determine the eigenvalues in these two cases, the exactness of the SWKB for these potentials is accounted for. Three non-exact cases are also analysed; the origin of this non-exactness is shown to be due the presence of additional singularities in $\sqrt{E-\omega^2(x)}$, like branch cuts in the $x-$plane.Comment: 11 pages, latex, 1 figure available on reques

Periodic Quasi - Exactly Solvable Models

Various quasi-exact solvability conditions, involving the parameters of the periodic associated Lam{\'e} potential, are shown to emerge naturally in the quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity of the Riccati type quantum Hamilton-Jacobi equation is primarily responsible for the surprisingly large number of allowed solvability conditions in the associated Lam{\'e} case. We also study the singularity structure of the quantum momentum function, which yields the band edge eigenvalues and eigenfunctions.Comment: 11 pages, 5 table

Quantum Hamilton-Jacobi analysis of PT symmetric Hamiltonians

We apply the quantum Hamilton-Jacobi formalism, naturally defined in the complex domain, to a number of complex Hamiltonians, characterized by discrete parity and time reversal (PT) symmetries and obtain their eigenvalues and eigenfunctions. Examples of both quasi-exactly and exactly solvable potentials are analyzed and the subtle differences, in the singularity structures of their quantum momentum functions, are pointed out. The role of the PT symmetry in the complex domain is also illustrated.Comment: 11 page

Accuracy of Semiclassical Methods for Shape Invariant Potentials

We study the accuracy of several alternative semiclassical methods by computing analytically the energy levels for many large classes of exactly solvable shape invariant potentials. For these potentials, the ground state energies computed via the WKB method typically deviate from the exact results by about 10%, a recently suggested modification using nonintegral Maslov indices is substantially better, and the supersymmetric WKB quantization method gives exact answers for all energy levels.Comment: 7 pages, Latex, and two tables in postscrip

Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton - Jacobi Formalism

We obtain the band edge eigenfunctions and the eigenvalues of solvable periodic potentials using the quantum Hamilton - Jacobi formalism. The potentials studied here are the Lam{\'e} and the associated Lam{\'e} which belong to the class of elliptic potentials. The formalism requires an assumption about the singularity structure of the quantum momentum function $p$, which satisfies the Riccati type quantum Hamilton - Jacobi equation, $p^{2} -i \hbar \frac{d}{dx}p = 2m(E- V(x))$ in the complex $x$ plane. Essential use is made of suitable conformal transformations, which leads to the eigenvalues and the eigenfunctions corresponding to the band edges in a simple and straightforward manner. Our study reveals interesting features about the singularity structure of $p$, responsible in yielding the band edge eigenfunctions and eigenvalues.Comment: 21 pages, 5 table

Measurement of the Neutron Radius of 208Pb Through Parity-Violation in Electron Scattering

We report the first measurement of the parity-violating asymmetry A_PV in the elastic scattering of polarized electrons from 208Pb. A_PV is sensitive to the radius of the neutron distribution (Rn). The result A_PV = 0.656 \pm 0.060 (stat) \pm 0.014 (syst) ppm corresponds to a difference between the radii of the neutron and proton distributions Rn - Rp = 0.33 +0.16 -0.18 fm and provides the first electroweak observation of the neutron skin which is expected in a heavy, neutron-rich nucleus.Comment: 6 pages, 1 figur

Multifrequency observation of the optically violent variable quasar 3C 446

Extensive optical and radio monitoring data and seven multifrequency spectra were obtained of the violently variable quasar 3C 446. The monitoring data suggest a correlation between the radio and optical outbursts, with the optical flare preceding the radio activity by 400-600 days. A difference in the statistical behavior of the optical and radio variability indicates that considerable processing occurs to the optical emitting plasma before it becomes radio emitting plasma. Within the radio band, outbursts proceed from high to low frequencies. An outburst in 1983 showed greater and more rapid variation in the optical than in the near-IR region. The 10-100 μm fluxes did not follow the higher frequency variation, suggesting a time delay between these spectral domains. During another time, the X-ray emission varied on a time scale of days and more rapidly than the UV or optical emission. On a time scale of weeks-months, the X-ray fluxes are well correlated with the UV-IR fluxes but not with the radio fluxes. The multifrequency data show that the flat radio spectrum turns over at 3-10 x 10^(11) Hz and the continuum steepens with frequency; ɑ(IR) = 1.1, ɑ(opt-UV) = -2 to -3. The X-ray emission lies an order of magnitude above an extrapolation of the optical-UV spectrum and has a harder spectrum. The power is primarily concentrated in the submillimeter and infrared region. When the source is faint, a blue bump may be present. The flux in the Lycx line is proportional to the UV continuum flux density when the source is bright but is independent of the continuum level when the source is faint. The data suggest that the X-rays are produced by the inverse Compton process from an emitting region (10^(16) cm) smaller than but related to the synchrotron emitting UV-IR region. The characteristic size of the emitting region increases with decreasing frequency from 10^(16) (X-ray region) to 1-3 x 10^(17) cm (far IR-submillimeter region) to 10^(19)-10^(20) cm (radio region). Plasma conditions are best constrained at the frequency when the source becomes transparent, the far IR-submillimeter band, where B ≈ 3-100 G, n ≈ 40-100 cm^(-3); and the Doppler boosting factor δ ≈ 1-5