Cilj ovog rada je pobliže upoznavanje s Diracovom jednadžbom koja opisuje ponašanje elektrona koji se giba relativističkom brzinom. Potaknut neuspjelim pokušajima fizičara da interpretiraju pojam negativne energije, Dirac je formirao svoju jednadžbu. Njegov rad i predviđanja su u to vrijeme bili revolucionarni. Svojim objašnjenjem pojma negativne energije je predvidio cijeli novi svijet sagrađen od antimaterije. Polazeći od Schrödingerove jednadžbe, preko Klein-Gordonove relativističke jednadžbe i njenih nedostataka dolazimo do Diracove jednadžbe i rješenja, koja je u konačnici rezultirala otkrićem pozitrona.

The aim of this thesis is to get acquainted with form of Dirac equation which describes the behaviour of an electron moving at a relativistic speed. Triggered by unsuccessful attempts by the physicist to interpret the concept of negative energy, Dirac formed his own equation. His work and predictions were revolutionary at that time. In his explanation of the concept of negative energy a whole new world of antimatter was predicted. Starting from Schrodinger's equation, through Klein Gordon's relativistic equation and its disadvantages we come to Dirac's equations and solutions, which ultimately resulted in the discovery of positron.