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Studies of relativistic quantum mechanics - The fundamentals of the Dirac equation and an analytical solution to hydrogen-like atoms
KTH, School of Engineering Sciences (SCI), Theoretical Physics.
KTH, School of Engineering Sciences (SCI), Theoretical Physics.
2015 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

In 1928, the brilliance of Paul Dirac granted him the insight to develop a particle equation that was fully consistent with both the principles of quantum mechanics and the theory of special relativity. In this bachelor thesis we have studied the fundamentals of relativistic quantum mechanics including the derivation of the Dirac equation in a similar fashion to the way originally done by Paul Dirac. Additionally we have studied the analytical solution for hydrogen-like atoms. Furthermore we have numerically analysed the energy spectrum, radial characteristics and correctional terms using programs written in Python and MATLAB. Finally we have investigated the implications and applications ofthe Dirac Hamiltonian and its use to effectively describe the attributes of gold atoms.

We find that relativistic contribution scales approximately by Z2 for large Z. In addition, we conclude that the Dirac Hamiltonian is of vital importance for an accurate description of chemical and physical properties of large atoms. Furthermore, we have completed calculations of the radial solution for the Coulomb potential and also for a free particle.

Abstract [sv]

År 1928 lyckades den enastående vetenskapsmannen Paul Dirac härleda en ekvation som var fullt hållbar inom både kvantmekanik och speciella relativitetsteorin. I detta kandidatexamensarbete har vi studerat de grundläggande principerna inom relativistisk kvantmekanik såsom härledningen av Dirac ekvationen som den ursprungligen gjordes av Paul Dirac. Vidare har vi undersökt den analytiska lösningen för väteliknande atomer. Detta följdes upp av en numerisk analys av energi spektrum, radiella delens utmärkande drag och korrektions termer med hjälp av program skrivna i Python och MATLAB. Slutligen har vi granskat implikationer och tillämpningar av Dirac hamiltonianen och dess möjligheter att beskriva guld atomens attribut.

Vi fann att de relativistiska bidragen ökar med ungefär Z2 för stora värden på Z. Vidare drog vi slutsatsen att Dirac hamiltonianen är av stor betydelse för en noggrann beskrivningav de kemiska och fysiska egenskaperna av guld atomen. Vi färdigställde sedan beräkningar av den radiella lösningen till Coulumb potentialen och för en fri partikel.

Place, publisher, year, edition, pages
2015.
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-168070OAI: oai:DiVA.org:kth-168070DiVA: diva2:814106
Supervisors
Available from: 2015-05-26 Created: 2015-05-26 Last updated: 2015-05-26Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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