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master's thesis
Učinci magnetskog polja na jednoelektronski spektar dvodimenzionalnog elektronskog plina
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:193438
Tomić, Kristina
University of Zagreb
Faculty of Science
Department of Physics

Institutional repository: Repository of the Faculty of Science

Cite this document

Tomić, K. (2016). Učinci magnetskog polja na jednoelektronski spektar dvodimenzionalnog elektronskog plina (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:193438

Tomić, Kristina. "Učinci magnetskog polja na jednoelektronski spektar dvodimenzionalnog elektronskog plina." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:193438

Tomić, Kristina. "Učinci magnetskog polja na jednoelektronski spektar dvodimenzionalnog elektronskog plina." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:193438

Tomić, K. (2016). 'Učinci magnetskog polja na jednoelektronski spektar dvodimenzionalnog elektronskog plina', Master's thesis, University of Zagreb, Faculty of Science, accessed 22 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:193438

Tomić K. Učinci magnetskog polja na jednoelektronski spektar dvodimenzionalnog elektronskog plina [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 November 22] Available at: https://urn.nsk.hr/urn:nbn:hr:217:193438

K. Tomić, "Učinci magnetskog polja na jednoelektronski spektar dvodimenzionalnog elektronskog plina", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:193438

Metadata
TitleUčinci magnetskog polja na jednoelektronski spektar dvodimenzionalnog elektronskog plina
Title (english)The influence of magnetic field on the one-electron spectrum of two-dimensional electron gas
AuthorKristina Tomić
MentorDanko Radić (mentor)
Committee memberDanko Radić (predsjednik povjerenstva)
Committee memberGorjana Jerbić-Zorc (član povjerenstva)
Committee memberDraginja Mrvoš-Sermek (član povjerenstva)
Committee memberTomica Hrenar (član povjerenstva)
Committee memberAna Sušac (član povjerenstva)
Committee memberTajana Preočanin (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Physics)
Zagreb
Defense date and country2016-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
U ovom diplomskom radu promatrali smo utjecaj magnetskog polja na dvodimenzionalni plin slobodnih elektrona, na elektron na dvodimenzionalnoj kristalnoj rešetci te na elektron na kvazi - jednodimenzionalnoj kristalnoj rešetci. Uveli smo magnetsko polje u sustav načelom minimalne supstitucije te opisali neke klasične aspekte polja poput magnetovodljivosti u okviru Sommerfeldovog modela metala. Proučavane su kvazi-klasične veličine poput elektronskih orbita u faznom prostoru i ciklotronske mase. U smislu kvantnomehaničkog opisa riješena je Schrödingerova jednadžba za elektron u magnetskom polju u tri karakteristične geometrije: slobodni elektron, elektron na pravokutnoj kristalnoj rešetci u okviru aproksimacije čvrste veze i elektron u kvazi-jednodimenzionalnoj geometriji te je izračunat pripadni jednoelektronski spektar i valne funkcije. Pokazano je da magnetsko polje ima fundamentalni učinak "jednodimenzionalizacije" elektronskog spektra, a na pravokutnoj rešetci vodi na pojavu iznimno kompleksnog spektra fraktalne strukture (tzv. "Hofstadterov leptir“). Također, iz sadržaja diplomskog rada, odabrana je prikladna tema koja je prilagođena za nastavni sat iz predmeta Fizika u prirodoslovnoj gimnaziji.
Abstract (english)
In this diploma thesis we considered the influence of the magnetic field on two-dimensional electron gas, the electrons on a two-dimensional lattice and the electrons in a quasi – one - dimensional lattice. We introduced the magnetic field in the system using the principle of minimal substitution and described some aspects of classical fields like magneto – conductance within the Sommerfeld model of metals. We have also studied the quasi-classical traits of the electron gas in the magnetic field like electronic orbits in the phase space and the cyclotron mass. In terms of quantum-mechanical description we solved the Schrödinger equation for the electron in the magnetic field in three characteristic geometries: free electron, electron on a rectangular lattice within the tight – binding approximation, and an electron in a quasi-one-dimensional geometry and calculated the corresponding one-electron energy spectrum and wave functions. We showed that the magnetic field has a fundamental effect of “one - dimensioning” the electronic spectrum, while the rectangular lattice leads to the occurrence of a highly complex spectrum with fractal structure (so-called "Hofstadter's butterfly"). Furthermore, we selected a suitable topic from the contents of this diploma thesis and adapted it to form a Physics lesson in the high school.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:193438
Study programmeTitle: Physics and Chemistry; specializations in: Education
Course: Education
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije fizike i kemije (magistar/magistra edukacije fizike i kemije)
Type of resourceText
File originBorn digital
Access conditionsOpen access
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Created on2017-03-05 12:45:43