25 research outputs found
Electric dipole and quadrupole contributions to valence electron binding in a charge-screening environment
We make a multipole expansion of the atomic/molecular electrostatic charge
distribution as seen by the valence electron up to the quadrupole term. The
Tridiagonal Representation Approach (TRA) is used to obtain an exact bound
state solution associated with an effective quadrupole moment and assuming that
the electron-molecule interaction is screened by suborbital electrons. We show
that the number of states available for binding the electron is finite forcing
an energy jump in its transition to the continuum that could be detected
experimentally in some favorable settings. We expect that our solution gives an
alternative, viable and simple description of the binding of valence
electron(s) in atoms/molecules with electric dipole and quadrupole moments. We
also ascertain that our model implies that a pure quadrupole-bound anion cannot
exist in such a charge-screening environment.Comment: 14 pages, 1 tabl
Infinite potential well with a sinusoidal bottom
We construct a tridiagonal matrix representation of the wave operator that
maps the wave equation into a three-term recursion relation for the expansion
coefficients of the wavefunction. Finding a solution of the recursion relation
is equivalent to solving the original problem. Consequently, a larger class of
solvable potentials is obtained. The usual diagonal representation constraint
results in a reduction to the conventional class of solvable potentials. To
exhibit the power of this approach, we give an exact solution for the infinite
potential well with sinusoidal bottom.Comment: 8 pages, 2 figures, 1 table Details will be published in Journal of
Mathematical Physics, Vol. 49, Issue 8 (August 2008
Relativistic Double Barrier Problem with Three Sub-Barrier Transmission Resonance Regions
We obtain exact scattering solutions of the Dirac equation in 1+1 dimensions
for a double square barrier vector potential. The potential floor between the
two barriers is higher than 2mc^2 whereas the top of the barriers is at least
2mc^2 above the floor. The relativistic version of the conventional double
barrier transmission resonance is obtained for energies within + or - mc^2 from
the height of the barriers. However, we also find two more (sub-barrier)
transmission resonance regions below the conventional one. Both are located
within the two Klein energy zones and characterized by resonances that are
broader than the conventional ones.Comment: 11 pages, 2 figures, one table (animations could be obtained from
first author
The Dirac-Coulomb Problem: a mathematical revisit
We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb
operator in a suitable complete square integrable basis. Orthogonal polynomials
techniques along with Darboux method are used to obtain the bound states energy
spectrum, the relativistic scattering amplitudes and phase shifts from the
asymptotic behavior of the polynomial solutions associated with the resulting
three-term recursion relation.Comment: 8 page