The energy level structure of a variety of one-dimensional confining potentials and the effects of a local singular perturbation

Motivated by current interest in quantum confinement potentials, especially with respect to the Stark spectroscopy of new types of quantum wells, we examine several novel one-dimensional singular oscillators. A Green function method is applied, the construction of the necessary resolvents is reviewed and several new ones are introduced. In addition, previous work on the singular harmonic oscillator model, introduced by Avakian et al. is reproduced to verify the method and results. A novel features is the determination of the spectra of asymmetric hybrid linear and quadratic potentials. As in previous work, the singular perturbations are modeled by delta functions.Comment: 14 pages, 10 figure

An Anomalous UV Extension in NGC6251

Deep U-band FOC images of the nuclear region of NGC6251 have revealed a region of extended emission which is most probably radiation scattered from a continuum source in the nucleus. This radiation lies interior to a dust ring, is nearly perpendicular to the radio jet axis, and is seen primarily in the FOC U and b filters. The extension has a low observed polarization($\le 10$), and is unlikely to arise from line emission. We know of no other examples similar to what we have found in NGC 6251, and we offer some tentative explanations. The nuclear morphology shows clear similarities to that seen in the nucleus of NGC 4261 except for the extended U-band radiation.Comment: 14 pages AAStex format + 4 figures; accepted for publication in ApJ Letter