155 research outputs found
The von Neumann-Wigner type potentials and the wave functions' asymptotics for the discrete levels in continuum
One to one correspondence between the decay law of the von Neumann-Wigner
type potentials and the asymptotic behaviour of the wave functions representing
bound states in the continuum is established.Comment: latex, 7 page
An "Accidental" Symmetry Operator for the Dirac Equation in the Coulomb Potential
On the basis of the generalization of the theorem about K-odd operators (K is
the Dirac's operator), certain linear combination is constructed, which appears
to commute with the Dirac Hamiltonian for Coulomb field. This operator
coincides with the Johnson and Lippmann operator and is intimately connected to
the familiar Laplace-Runge-Lenz vector. Our approach guarantees not only
derivation of Johnson-Lippmann operator, but simultaneously commutativity with
the Dirac Hamiltonian follows.Comment: 6 page
GPCR-OKB: the G protein coupled receptor oligomer knowledge base
Rapid expansion of available data about G Protein Coupled Receptor (GPCR) dimers/oligomers over the past few years requires an effective system to organize this information electronically. Based on an ontology derived from a community dialog involving colleagues using experimental and computational methodologies, we developed the GPCR-Oligomerization Knowledge Base (GPCR-OKB). GPCR-OKB is a system that supports browsing and searching for GPCR oligomer data. Such data were manually derived from the literature. While focused on GPCR oligomers, GPCR-OKB is seamlessly connected to GPCRDB, facilitating the correlation of information about GPCR protomers and oligomers
What is the boundary condition for radial wave function of the Schr\"odinger equation ?
There is much discussion in the mathematical physics literature as well as in
quantum mechanics textbooks on spherically symmetric potentials. Nevertheless,
there is no consensus about the behavior of the radial function at the origin,
particularly for singular potentials. A careful derivation of the radial
Schr\"odinger equation leads to the appearance of a delta function term when
the Laplace operator is written in spherical coordinates. As a result,
regardless of the behavior of the potential, an additional constraint is
imposed on the radial wave function in the form of a vanishing boundary
condition at the origin.Comment: 15 page
On the regularization scheme and gauge choice ambiguities in topologically massive gauge theories
It is demonstrated that in the (2+1)-dimensional topologically massive gauge
theories an agreement of the Pauli-Villars regularization scheme with the other
schemes can be achieved by employing pairs of auxiliary fermions with the
opposite sign masses. This approach does not introduce additional violation of
discrete (P and T) symmetries. Although it breaks the local gauge symmetry only
in the regulator fields' sector, its trace disappears completely after removing
the regularization as a result of superrenormalizability of the model. It is
shown also that analogous extension of the Pauli-Villars regularization in the
vector particle sector can be used to agree the arbitrary covariant gauge
results with the Landau ones. The source of ambiguities in the covariant gauges
is studied in detail. It is demonstrated that in gauges that are softer in the
infrared region (e.g. Coulomb or axial) nonphysical ambiguities inherent to the
covariant gauges do not arise.Comment: Latex, 13 pages. Replaced mainly to change preprint references to
journal one
New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to Separation of Variables
The supersymmetric intertwining relations with second order supercharges
allow to investigate new two-dimensional model which is not amenable to
standard separation of variables. The corresponding potential being the
two-dimensional generalization of well known one-dimensional P\"oschl-Teller
model is proven to be exactly solvable for arbitrary integer value of parameter
all its bound state energy eigenvalues are found analytically, and the
algorithm for analytical calculation of all wave functions is given. The shape
invariance of the model and its integrability are of essential importance to
obtain these results.Comment: 23 page
- …