Hartree-Fock methods and overview of material
Contents
Overview of lectures
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
Exercise 2: Matrix elements for the Hartree-Fock method and the nuclear shell model
Project 3: Developing a Hartree-Fock program
Hartree-Fock methods and overview of material
Morten Hjorth-Jensen
[1, 2]
[1]
National Superconducting Cyclotron Laboratory
and
Department of Physics and Astronomy
,
Michigan State University
, East Lansing, MI 48824, USA
[2]
Department of Physics, University of Oslo, N-0316 Oslo, Norway
28th Indian-Summer School on Ab Initio Methods in Nuclear Physics
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© 2013-2016, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license