Some recent results on contact or point supported potentials
- URL: http://arxiv.org/abs/2005.09931v1
- Date: Wed, 20 May 2020 09:31:16 GMT
- Title: Some recent results on contact or point supported potentials
- Authors: Luis M. Nieto, Manuel Gadella, Juan M. Mateos-Guilarte, Jose M.
Munoz-Castaneda, and Cesar Romaniega
- Abstract summary: We introduce some contact potentials that can be written as a linear combination of the Dirac delta and its first derivative.
The dependence of energy bands with the parameters (coefficients of the deltas) can be computed numerically.
A $delta$-$delta'$ interaction is used to approximate a potential of wide use in nuclear physics.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We introduced some contact potentials that can be written as a linear
combination of the Dirac delta and its first derivative, the
$\delta$-$\delta'$ interaction. After a simple general presentation in one
dimension, we briefly discuss a one dimensional periodic potential with a
$\delta$-$\delta'$ interaction at each node. The dependence of energy bands
with the parameters (coefficients of the deltas) can be computed numerically.
We also study the $\delta$-$\delta'$ interaction supported on spheres of
arbitrary dimension. The spherical symmetry of this model allows us to obtain
rigorous conclusions concerning the number of bound states in terms of the
parameters and the dimension. Finally, a $\delta$-$\delta'$ interaction is used
to approximate a potential of wide use in nuclear physics, and estimate the
total number of bound states as well as the behaviour of some resonance poles
with the lowest energy.
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