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Variational approach to the many-body problem with error estimation

Rogius Svensson, Claes LU (2018) PHYM01 20172
Mathematical Physics
Department of Physics
Abstract
In this thesis a method for doing approximate calculations of the ground state of quantum mechanical many-body systems is developed and implemented. This method uses the Hartree-Fock method as a starting point and approximates the ground state as a linear combination of non-orthogonal Slater determinants. The Slater determinants are added consecutively by minimising their associated energy while keeping the previously found Slater determinants fixed. This method was tested on a quantum harmonic oscillator filled with interacting fermions and was found to give good approximations to the ground state of this system with only a few Slater determinants. Error estimation of the approximated ground state is done by calculating the energy... (More)
In this thesis a method for doing approximate calculations of the ground state of quantum mechanical many-body systems is developed and implemented. This method uses the Hartree-Fock method as a starting point and approximates the ground state as a linear combination of non-orthogonal Slater determinants. The Slater determinants are added consecutively by minimising their associated energy while keeping the previously found Slater determinants fixed. This method was tested on a quantum harmonic oscillator filled with interacting fermions and was found to give good approximations to the ground state of this system with only a few Slater determinants. Error estimation of the approximated ground state is done by calculating the energy variance. The energy variance was used in two different methods for improving upon the approximated energy, both of which was found to work well. (Less)
Popular Abstract (Swedish)
I detta arbetet utvecklas en metod för att göra approximativa beräkningar av grundtillståndet för ett kvantmekaniskt system bestående av flera partiklar.
Please use this url to cite or link to this publication:
author
Rogius Svensson, Claes LU
supervisor
organization
course
PHYM01 20172
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Many-body problems, Slater determinants, variational approach
language
English
id
8954381
date added to LUP
2018-08-13 08:29:20
date last changed
2018-08-13 08:29:20
@misc{8954381,
  abstract     = {{In this thesis a method for doing approximate calculations of the ground state of quantum mechanical many-body systems is developed and implemented. This method uses the Hartree-Fock method as a starting point and approximates the ground state as a linear combination of non-orthogonal Slater determinants. The Slater determinants are added consecutively by minimising their associated energy while keeping the previously found Slater determinants fixed. This method was tested on a quantum harmonic oscillator filled with interacting fermions and was found to give good approximations to the ground state of this system with only a few Slater determinants. Error estimation of the approximated ground state is done by calculating the energy variance. The energy variance was used in two different methods for improving upon the approximated energy, both of which was found to work well.}},
  author       = {{Rogius Svensson, Claes}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Variational approach to the many-body problem with error estimation}},
  year         = {{2018}},
}