NUMERICAL CALCULATION OF THE GROUND STATE ENERGIES OF THE HYDROGEN MOLECULE AND THE HELIUM ATOM USING QUANTUM MONTE CARLO METHODS

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dc.contributor.authorSULEIMAN, ABDUSSALAM BALARABE
dc.date.accessioned2014-03-07T08:37:35Z
dc.date.available2014-03-07T08:37:35Z
dc.date.issued2012-02
dc.descriptionA DISSERTATION SUBMITTED TO THE POST GRADUATE SCHOOL, AHMADU BELLO UNIVERSITY, ZARIA NIGERIA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF THE DEGREEOF DOCTOR OF PHILOSOPHY IN PHYSICS (THEORETICAL CONDENSED MATTER PHYSICS) DEPARTMENT OF PHYSICS, AHMADU BELLO UNIVERSITY, ZARIA NIGERIA FEBRUARY, 2012en_US
dc.description.abstractThe ground state energies of Hydrogen molecule and the Helium atom are numerically evaluated using the Variational Quantum Monte Carlo [VQMC] and the Path Integral Monte Carlo [PIMC]. These analysis are done under the context of the accuracy of Born-Oppenhiemer approximation [fixed nuclei restriction]. The ground state energies of hydrogen molecule for different interproton separations (0.4 – 1.0Å) are computed using the two different methods mentioned [VQMC and PIMC] and compared with previous numerical and empirical results (results obtained by other reviewers in the field) that are essentially exact. The results from the Path Integral Monte Carlo method of calculation were found to be precisely approaching the required order of accuracy i.e. -31.92eV in the case of hydrogen molecule. The VQMC and PIMC were applied to the helium atom at different values of the variational parameter b while the interproton separation was set to zero. The corresponding average values of the ground state energy is found to be -78.94eV and compared with the standard values and also with values obtained from other reviewers in the field. This also shows that results obtained from PIMC are much reliable and approaches the exact values i.e. -78.96eV. The standard errors in both cases were calculated and the effect of time step [PIMC] as per the ground state energies is also observed.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/3485
dc.language.isoenen_US
dc.subjectNUMERICAL,en_US
dc.subjectCALCULATION,en_US
dc.subjectGROUND,en_US
dc.subjectSTATE,en_US
dc.subjectENERGIES,en_US
dc.subjectHYDROGEN,en_US
dc.subjectMOLECULE,en_US
dc.subjectHELIUM,en_US
dc.subjectATOM,en_US
dc.subjectUSING,en_US
dc.subjectQUANTUM,en_US
dc.subjectMONTE,en_US
dc.subjectCARLO,en_US
dc.subjectMETHODS,en_US
dc.titleNUMERICAL CALCULATION OF THE GROUND STATE ENERGIES OF THE HYDROGEN MOLECULE AND THE HELIUM ATOM USING QUANTUM MONTE CARLO METHODSen_US
dc.typeThesisen_US
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