7,524 research outputs found
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
Heisenberg-type higher order symmetries of superintegrable systems separable in cartesian coordinates
Heisenberg-type higher order symmetries are studied for both classical and
quantum mechanical systems separable in cartesian coordinates. A few particular
cases of this type of superintegrable systems were already considered in the
literature, but here they are characterized in full generality together with
their integrability properties. Some of these systems are defined only in a
region of , and in general they do not include bounded solutions.
The quantum symmetries and potentials are shown to reduce to their
superintegrable classical analogs in the limit.Comment: 23 Pages, 3 figures, To appear in Nonlinearit
- …