Hartree-Fock
Contents
Why Hartree-Fock?
Why Hartree-Fock?
Definitions and notations
Definitions and notations
Definitions and notations
Definitions and notations
Definitions and notations
Brief reminder on some linear algebra properties
Basic Matrix Features
Basic Matrix Features
Basic Matrix Features, simple \( 2 \times 2 \) determinant
Definitions and notations
Definitions and notations
Definitions and notations
Definitions and notations
Definitions and notations
Definitions and notations
Definitions and notations
Definitions and notations
Definitions and notations
Definitions and notations
Definitions and notations
Compact functional
Properties of the interaction elements
Redefining the matrix elements
Rewriting the energy functional
Reminder on Variational Calculus and Lagrangian Multipliers
Variational Calculus and Lagrangian Multipliers, simple example
Manipulating terms
Adding the Lagrangian multiplier
And with the Euler-Lagrange equations we get
Hartree-Fock by varying the coefficients of a wave function expansion
More on linear algebra
Coefficients of a wave function expansion
More Basic Matrix Features, simple \( 2 \times 2 \) determinant, useful property of determinants
More Basic Matrix Features, \( n \times n \) determinant
More Basic Matrix Features, a general \( n \times n \) determinant
A general Slater determinant
Hartree-Fock by varying the coefficients of a wave function expansion
Hartree-Fock by varying the coefficients of a wave function expansion
Hartree-Fock by varying the coefficients of a wave function expansion
Hartree-Fock by varying the coefficients of a wave function expansion
Hartree-Fock by varying the coefficients of a wave function expansion
Hartree-Fock by varying the coefficients of a wave function expansion
Hartree-Fock by varying the coefficients of a wave function expansion
Hartree-Fock by varying the coefficients of a wave function expansion
Hartree-Fock algorithm
Hartree-Fock algorithm
Hartree-Fock algorithm
Hartree-Fock algorithm
Analysis of Hartree-Fock equations and Koopman's theorem
Analysis of Hartree-Fock equations and Koopman's theorem
Analysis of Hartree-Fock equations and Koopman's theorem
Analysis of Hartree-Fock equations and Koopman's theorem
Analysis of Hartree-Fock equations and Koopman's theorem
Analysis of Hartree-Fock equations and Koopman's theorem
Analysis of Hartree-Fock equations, Koopman's theorem
Analysis of Hartree-Fock equations and Koopman's theorem
Analysis of Hartree-Fock equations and Koopman's theorem
Analysis of Hartree-Fock equations and Koopman's theorem
Analysis of Hartree-Fock equations and Koopman's theorem
Analysis of Hartree-Fock equations and Koopman's theorem
Exercise 1: Hartree-Fock Slater determinant
Developing a Hartree-Fock program
Developing a Hartree-Fock program, the algorithm
Developing a Hartree-Fock program, the density matrix
Developing a Hartree-Fock program, additional considerations
"Developing a Hartree-Fock program, a simple Python program":"https://github.com/NuclearTalent/NuclearStructure/tree/master/doc/Programs/HFcode"
Developing a Hartree-Fock program, a simple Python program and input files
"Developing a Hartree-Fock program, the simple Python program":"https://github.com/NuclearTalent/NuclearStructure/tree/master/doc/Programs/HFcode"
Developing a Hartree-Fock program, analyzing the results
Developing a Hartree-Fock program, separation energies
Analyzing the results in terms of the nuclear force components
Reminder on definitions
A general Hamiltonian
Adding a three-body interaction
An additional reminder
Modification due to a three-body force
The monopole term
More on the monopole term
Linking the monopole part with Hartree-Fock theory
Linking the monopole part with Hartree-Fock theory, angular momentum
Linking the monopole part with Hartree-Fock theory, more definitions
Final expressions for the monopole term
Analyzing our results, decomposing the Hamiltonian
Analyzing our results, decomposing the Hamiltonian
Analyzing our results, decomposing the Hamiltonian
Analyzing our results, decomposing the Hamiltonian
Analyzing our results, decomposing the Hamiltonian
Hartree-Fock
Morten Hjorth-Jensen
National Superconducting Cyclotron Laboratory
and
Department of Physics and Astronomy
,
Michigan State University
, East Lansing, MI 48824, USA
Jul 20, 2017
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© 2013-2017, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license