Excited States in Variational Many-Body Approaches
(2018) PHYM01 20181Mathematical Physics
Department of Physics
- Abstract
- A method is implemented wherein numerical approximations to the ground
and first few excited states of a quantum mechanical N -body 1D harmonic
oscillator are found through variational methods, representing the states as a
linear combination of normalized pseudo-states which are themselves linear
combinations of non-orthogonal Slater determinants. These states are then
used as a low energy basis for configuration interaction. An expression is
derived for an analytical matrix derivative of the energy functional, in order
to improve the speed of the variation.
The speed and accuracy using the analytical derivative is compared to
that of the numerical derivative, and a number of different gradient descent
methods are tried and... (More) - A method is implemented wherein numerical approximations to the ground
and first few excited states of a quantum mechanical N -body 1D harmonic
oscillator are found through variational methods, representing the states as a
linear combination of normalized pseudo-states which are themselves linear
combinations of non-orthogonal Slater determinants. These states are then
used as a low energy basis for configuration interaction. An expression is
derived for an analytical matrix derivative of the energy functional, in order
to improve the speed of the variation.
The speed and accuracy using the analytical derivative is compared to
that of the numerical derivative, and a number of different gradient descent
methods are tried and compared. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/8963534
- author
- Gustafsson, David LU
- supervisor
- organization
- course
- PHYM01 20181
- year
- 2018
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- quantum mechanics, many-body problems, excited states, Hartree-Fock method, variational method, VAMPIR
- language
- English
- id
- 8963534
- date added to LUP
- 2018-12-18 14:13:13
- date last changed
- 2018-12-18 14:13:13
@misc{8963534, abstract = {{A method is implemented wherein numerical approximations to the ground and first few excited states of a quantum mechanical N -body 1D harmonic oscillator are found through variational methods, representing the states as a linear combination of normalized pseudo-states which are themselves linear combinations of non-orthogonal Slater determinants. These states are then used as a low energy basis for configuration interaction. An expression is derived for an analytical matrix derivative of the energy functional, in order to improve the speed of the variation. The speed and accuracy using the analytical derivative is compared to that of the numerical derivative, and a number of different gradient descent methods are tried and compared.}}, author = {{Gustafsson, David}}, language = {{eng}}, note = {{Student Paper}}, title = {{Excited States in Variational Many-Body Approaches}}, year = {{2018}}, }