Scattering Theory for 2N Parameter Models of Finitely Many Relativistic δ-Sphere and δ-Sphere plus Coulomb Interactions Supported by Concentric Spheres in Quantum Mechanics

Advances in Mathematical Physics ◽

10.1155/2020/5825397 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

A. Vyabandi ◽

J. Shabani

Keyword(s):

Quantum Mechanics ◽

Scattering Theory ◽

Spectral Properties ◽

Scattering Data ◽

Coulomb Interactions ◽

Resolvent Equations ◽

Concentric Spheres ◽

Mathematical Definitions

We study scattering theory for 2N parameter models of finitely many relativistic δ-sphere and δ-sphere plus Coulomb interactions. We provide the mathematical definitions of the Hamiltonians, solve the resolvent equations, and compute the nonrelativistic limits for both models. We obtain new results related to spectral properties and scattering data.

Download Full-text

Characterization of the scattering data in multidimensional inverse scattering theory

Inverse Problems ◽

10.1088/0266-5611/7/3/011 ◽

1991 ◽

Vol 7 (3) ◽

pp. 461-489 ◽

Cited By ~ 12

Author(s):

R Weder

Keyword(s):

Inverse Scattering ◽

Scattering Theory ◽

Scattering Data ◽

Inverse Scattering Theory

Download Full-text

Exploiting the full quantum crystallography

Canadian Journal of Chemistry ◽

10.1139/cjc-2017-0667 ◽

2018 ◽

Vol 96 (7) ◽

pp. 599-605 ◽

Cited By ~ 8

Author(s):

Lou Massa ◽

Chérif F. Matta

Keyword(s):

Quantum Mechanics ◽

Electron Density ◽

Mathematical Structure ◽

Scattering Data ◽

X Ray ◽

X Ray Crystallography ◽

X Ray Scattering ◽

Fundamental Value ◽

Quantum Crystallography ◽

Ray Scattering

Quantum crystallography (QCr) is a branch of crystallography aimed at obtaining the complete quantum mechanics of a crystal given its X-ray scattering data. The fundamental value of obtaining an electron density matrix that is N-representable is that it ensures consistency with an underlying properly antisymmetrized wavefunction, a requirement of quantum mechanical validity. However, X-ray crystallography has progressed in an impressive way for decades based only upon the electron density obtained from the X-ray scattering data without the imposition of the mathematical structure of quantum mechanics. Therefore, one may perhaps ask regarding N-representability “why bother?” It is the purpose of this article to answer such a question by succinctly describing the advantage that is opened by QCr.

Download Full-text