Osnovno stanje atoma berilija u Hertreejevoj i Hartree-Fockovoj aproksimaciji

master's thesis

• Title (english): Ground State of Berilium Atom in Hartre and Hartree-Fock Approximation
• Author: Mladen Špoljar
• Mentor: Ivo Batistić (mentor)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2015-02-16, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

U ovom radu izračunavam osnovno stanje atoma berilija primjenom nekoliko različitih aproksimativnih varijacijskih računa. Kao varijacijske valne funkcije koriste se Hartreejeva aproksimacija (HA) gdje se osnovno stanje aproksimira produktom jednočestičnih valnih funkcija , te Hartree-Fockovoa aproksimacija (HFA) gdje je valna funkcija dana kao antisimetrizirani produkt jednočestičnih valnih funkcija odnosno tzv. Slaterovom determinantom. Daljnja pojednostavljene koje koristim je da su stanja elektrona sferno simetričan te da su po dva elektrona u 1s, a dva u 2s stanju. Za elektrone u istom orbitalnom stanju pretpostavljam da imaju suprotne spinove. U prva dva izračuna stanja elektrona su dana s zasjenjenim Bohrovim orbitalama (BO) pa energija ovisi samo o nekoliko realnih parametara tzv. zasjenjenih naboja. Vrijednosti tih parametara se dobiju minimalizacijom energije. U druga dva izračuna, varijacija metoda vodi na diferencijalne jednadžbe tzv. Hartreejeve jednadžbe (HJ) i Hartree-Fock jednadžbe (HFJ) za stanja elektrona. Ove sam jednadžbe rješava numeričkim postupcima koja se uobičajeno nazivaju FDH (finite difference Hartree) i FDHF (finite difference Hartree-Fock). Svi dobiveni rezultati odstupaju do nekoliko postotaka od eksperimentalne vrijednosti energije osnovnog stanja.

Abstract (english)

In this thesis I have calculated the ground state of beryllium atom by using several approximate variational methods. The variational wave function for the ground state in Hartree approximation (HA) is a product of single particle wave functions, while in Hartree-Fock approximation (HFA) wave function is an antisymmetrized product of single particle wave functions i.e. Slatter determinant (SD). A further simplification is assumption of spherically symmetric single electron states. In HA and HFA two of four electrons are placed in 1s state and other two in 2s state with assumption that electrons in the same orbital state have opposite spin. In mine first two calculations single electron states are screened Bohr orbitals with several variational parameters i.e. screened charges. Values of the variational parameters (screened charges) were determined by minimization of total energy. In mine next two calculations I have solved numerically Hartree and Hartree-Fock differential equations by using finite difference HA (FDH) and finite difference HFA (FDHF) methods. All results for total energy of ground state beryllium atom differ from experimental value by at most few percent.

• Keywords: Hartreejeva aproksimacija (HA); Hartree-Fockovoa aproksimacija (HFA)
• Keywords (english): Hartree approximation (HA); Hartree-Fock approximation (HFA)
• Language: croatian
• URN:NBN: urn:nbn:hr:217:622753
• Study programme: Title: Physics; specializations in: Research; Course: Research; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-08-22 10:30:43