Slow electron elastic scattering by a target represented by different
zero-range potentials
- URL: http://arxiv.org/abs/2206.08693v1
- Date: Fri, 17 Jun 2022 11:25:48 GMT
- Title: Slow electron elastic scattering by a target represented by different
zero-range potentials
- Authors: A. S. Baltenkov and I. Woiciechowski
- Abstract summary: The phase shifts of wave function of a particle scattering on a target formed by a pair of non-identical zero-range potentials are calculated.
The special features of the S-matrix method for the case of arbitrary non-spherical potentials are discussed.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The general formulas to calculate the phase shifts of wave function of a
particle scattering on a target formed by a pair of non-identical zero-range
potentials are derived. It is shown that at asymptotically great distances from
the target the continuum wave function of particle is presented as an expansion
in a set of other than spherical, orthonormal functions. General formulas for
these functions are obtained. The special features of the S-matrix method for
the case of arbitrary non-spherical potentials are discussed.
Related papers
- Special functions in quantum phase estimation [61.12008553173672]
We focus on two special functions. One is prolate spheroidal wave function, which approximately gives the maximum probability that the difference between the true parameter and the estimate is smaller than a certain threshold.
The other is Mathieu function, which exactly gives the optimum estimation under the energy constraint.
arXiv Detail & Related papers (2023-02-14T08:33:24Z) - Dynamical chaos in nonlinear Schr\"odinger models with subquadratic
power nonlinearity [137.6408511310322]
We deal with a class of nonlinear Schr"odinger lattices with random potential and subquadratic power nonlinearity.
We show that the spreading process is subdiffusive and has complex microscopic organization.
The limit of quadratic power nonlinearity is also discussed and shown to result in a delocalization border.
arXiv Detail & Related papers (2023-01-20T16:45:36Z) - Non-collinear density functional theory [15.872687786457826]
This approach satisfies the correct collinear limit for any kind of functionals.
It has well-defined and numerically stable functional derivatives.
It provides local torque, hinting at its applications in spin dynamics.
arXiv Detail & Related papers (2021-10-17T09:39:09Z) - Effective Range Expansion for Describing a Virtual State [0.0]
We find the wave function inside the potential, and extending the solution with the region outside the range of potential.
The wave function outside the range of potential can be expanded in terms of spherical bessel and neumann function.
arXiv Detail & Related papers (2021-09-07T04:04:53Z) - Deformed Explicitly Correlated Gaussians [58.720142291102135]
Deformed correlated Gaussian basis functions are introduced and their matrix elements are calculated.
These basis functions can be used to solve problems with nonspherical potentials.
arXiv Detail & Related papers (2021-08-10T18:23:06Z) - Wigner time delay of a particle elastically scattered by a cluster of
zero-range potentials [0.0]
The Wigner time delay of slow particles in the process of their elastic scattering by complex targets is investigated.
The Huygens-Fresnel interference pattern formed by spherical waves emitted by each of the potentials is transformed into a system of spherical waves generated by the center of the target.
General formulas that connect the s-phase shifts of particle scattering by each of the zero-range potentials with the phases of particle scattering by the potential cluster forming the target are obtained.
arXiv Detail & Related papers (2021-07-13T11:36:20Z) - Functional integral method for potential scattering amplitude in quantum
mechanics [0.0]
We will obtain the potential scattering amplitude form the complete Green function in the corresponding external field through solving the Schrodinger equation.
Consider specific external potentials such as the Yukawa or Gaussian potential, we will find the corresponding differential scattering cross-sections.
arXiv Detail & Related papers (2021-04-02T01:16:51Z) - Exact thermal properties of free-fermionic spin chains [68.8204255655161]
We focus on spin chain models that admit a description in terms of free fermions.
Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
arXiv Detail & Related papers (2021-03-30T13:15:44Z) - Dynamical formulation of low-energy scattering in one dimension [0.0]
A transfer matrix $mathbfM$ of a short-range potential may be expressed in terms of the time-evolution operator for an effective two-level quantum system.
We explore the utility of this formulation in the study of the low-energy behavior of the scattering data.
arXiv Detail & Related papers (2021-02-11T15:55:34Z) - Weak asymptotics of wave function for N-particle system and asymptotic
filtering [0.0]
The phenomenon of scattering is discovered, which consists in the fact that only scattering processes contribute to the leading terms of such a representation.
The obtained representations are used to construct the corrects of the partial components of the wave function of $N$ particles in the hyperspherical representation.
arXiv Detail & Related papers (2020-10-11T18:59:30Z) - Paraxial wave function and Gouy phase for a relativistic electron in a
uniform magnetic field [68.8204255655161]
A connection between quantum mechanics and paraxial equations is established for a Dirac particle in external fields.
The paraxial form of the Landau eigenfunction for a relativistic electron in a uniform magnetic field is determined.
arXiv Detail & Related papers (2020-03-08T13:14:44Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.