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undergraduate thesis
Numeričko rješavanje Gross-Pitaevskiijeve jednadžbe u dvije dimenzije
Split: University of Split, University of Split, Faculty of science, 2022. urn:nbn:hr:166:596218
Poparić, Ivan
University of Split
Faculty of Science
Department of Physics

Institutional repository: Repository of Faculty of Science

Cite this document

Poparić, I. (2022). Numeričko rješavanje Gross-Pitaevskiijeve jednadžbe u dvije dimenzije (Undergraduate thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:596218

Poparić, Ivan. "Numeričko rješavanje Gross-Pitaevskiijeve jednadžbe u dvije dimenzije." Undergraduate thesis, University of Split, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:166:596218

Poparić, Ivan. "Numeričko rješavanje Gross-Pitaevskiijeve jednadžbe u dvije dimenzije." Undergraduate thesis, University of Split, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:166:596218

Poparić, I. (2022). 'Numeričko rješavanje Gross-Pitaevskiijeve jednadžbe u dvije dimenzije', Undergraduate thesis, University of Split, Faculty of Science, accessed 14 November 2024, https://urn.nsk.hr/urn:nbn:hr:166:596218

Poparić I. Numeričko rješavanje Gross-Pitaevskiijeve jednadžbe u dvije dimenzije [Undergraduate thesis]. Split: University of Split, Faculty of Science; 2022 [cited 2024 November 14] Available at: https://urn.nsk.hr/urn:nbn:hr:166:596218

I. Poparić, "Numeričko rješavanje Gross-Pitaevskiijeve jednadžbe u dvije dimenzije", Undergraduate thesis, University of Split, Faculty of Science, Split, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:166:596218

Metadata
TitleNumeričko rješavanje Gross-Pitaevskiijeve jednadžbe u dvije dimenzije
Title (english)Numerical solutions to the Gross-Pitaevskii equation in two dimensions
AuthorIvan Poparić
MentorPetar Stipanović (mentor)
Committee memberPetar Stipanović (predsjednik povjerenstva)
Committee memberLeandra Vranješ Markić (član povjerenstva)
Committee memberIvana Weber (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Physics)
Split
Defense date and country2022-09-15, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
Gross-Pitaevskiijeva jednadžba opisuje ponašanje bozona u Bose–Einsteinovom kondenzatu pri apsolutnoj nuli. Jednadžba je nelinearna i nije analitički rješiva, zbog čega se služimo numeričkim metodama. Cilj ovoga rada je riješiti vremenski ovisnu Gross-Pitaevskiijevu jednadžbu za kondenzat u sferno simetričnoj harmonijskoj magnetskoj zamci u dvije dimenzije i dobiti uvid u oblik valne funkcije stacionarnog stanja za privlačne i odbojne interakcije između bozona. Za potrebe numeričkog rješavanja diskretizira se domena valne funkcije i pronalazi algoritam za rješavanje jednadžbe. Rješenja su uspoređena s postojećom literaturom.
Abstract (english)
The Gross-Pitaevskii equation describes the behavior of bosons in the Bose–Einstein condensate at absolute zero. The equation is non-linear and cannot be solved analytically, which is why we use numerical methods. The aim of this thesis is to solve the time-dependent Gross-Pitaevskii equation for a condensate in a spherically symmetric harmonic magnetic trap in two dimensions and to gain insight into the shape of the stationary state wave function for attractive and repulsive interactions between bosons. For the purposes of finding a numerical solution, the domain of the wave function is discretized and an algorithm for solving the equation is found. The solutions are compared with existing literature.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:596218
Study programmeTitle: Physics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) fizike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
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Created on2022-11-04 13:05:29