FACTORIZATION OF THE MATRIX ELEMENTS OF THREE-ELECTRON OPERATORS USED IN CONFIGURATION-INTERACTION STUDIES OF THE ATOMICfSHELL

1996 ◽  
Vol 62 (1) ◽  
pp. 51-75 ◽  
Author(s):  
B.R. JUDD ◽  
EDWIN LO
Keyword(s):  
Configuration Interaction ◽  
Matrix Elements ◽  
Interaction Studies ◽  
The Matrix

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

Configuration interaction studies on the spectroscopic properties of PbO including spin–orbit coupling

2016 ◽  
Vol 25 (7) ◽  
pp. 073101 ◽  
Author(s):  
Wang Luo ◽  
Rui Li ◽  
Zhiqiang Gai ◽  
RuiBo Ai ◽  
Hongmin Zhang ◽  
...  
Keyword(s):  
Configuration Interaction ◽  
Spectroscopic Properties ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Interaction Studies

Spin-extended and configuration-interaction studies of first-row atoms

2009 ◽  
Vol 2 (S2) ◽  
pp. 13-20 ◽  
Author(s):  
Uzi Kaldor ◽  
Henry F. Schaefer ◽  
Frank E. Harris
Keyword(s):  
Configuration Interaction ◽  
Interaction Studies

Notizen: The Dipole Moment Function of HF Molecule Using Morse Potential

1977 ◽  
Vol 32 (8) ◽  
pp. 897-898 ◽  
Author(s):  
Y. K. Chan ◽  
B. S. Rao
Keyword(s):  
Wave Equation ◽  
Dipole Moment ◽  
Potential Function ◽  
Electric Dipole ◽  
Morse Potential ◽  
Moment Function ◽  
Matrix Elements ◽  
The Matrix ◽  
Vibration Rotation ◽  
Experimental Values

Abstract The radial Schrödinger wave equation with Morse potential function is solved for HF molecule. The resulting vibration-rotation eigenfunctions are then used to compute the matrix elements of (r - re)n. These are combined with the experimental values of the electric dipole matrix elements to calculate the dipole moment coefficients, M 1 and M 2.

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