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undergraduate thesis
Analiza kvantnih dimera opisanih modificiranim Lennard-Jonesovim potencijalom
Split: University of Split, Faculty of Science, 2024. urn:nbn:hr:166:085509
Šiklić, Toma
University of Split
Faculty of Science
Department of Physics

Institutional repository: Repository of Faculty of Science

Cite this document

Šiklić, T. (2024). Analiza kvantnih dimera opisanih modificiranim Lennard-Jonesovim potencijalom (Undergraduate thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:085509

Šiklić, Toma. "Analiza kvantnih dimera opisanih modificiranim Lennard-Jonesovim potencijalom." Undergraduate thesis, University of Split, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:166:085509

Šiklić, Toma. "Analiza kvantnih dimera opisanih modificiranim Lennard-Jonesovim potencijalom." Undergraduate thesis, University of Split, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:166:085509

Šiklić, T. (2024). 'Analiza kvantnih dimera opisanih modificiranim Lennard-Jonesovim potencijalom', Undergraduate thesis, University of Split, Faculty of Science, accessed 27 September 2024, https://urn.nsk.hr/urn:nbn:hr:166:085509

Šiklić T. Analiza kvantnih dimera opisanih modificiranim Lennard-Jonesovim potencijalom [Undergraduate thesis]. Split: University of Split, Faculty of Science; 2024 [cited 2024 September 27] Available at: https://urn.nsk.hr/urn:nbn:hr:166:085509

T. Šiklić, "Analiza kvantnih dimera opisanih modificiranim Lennard-Jonesovim potencijalom", Undergraduate thesis, University of Split, Faculty of Science, Split, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:166:085509

Metadata
TitleAnaliza kvantnih dimera opisanih modificiranim Lennard-Jonesovim potencijalom
Title (english)Analysis of quantum dimers described by modified Lennard-Jones potential
AuthorToma Šiklić
MentorPetar Stipanović (mentor)
Committee memberPetar Stipanović (predsjednik povjerenstva)
Committee memberLucija Krce (član povjerenstva)
Committee memberIvana Weber (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Physics)
Split
Defense date and country2024-09-19, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
Najpopularniji model potencijala dviju čestica, Lennard-Jonesov (12-6) potencijal, sačinjen je od kratkodosežnog odbojnog dijela te dugodosežnog privlačnog dijela. Ovaj završni rad ispituje kako potencija kratkodosežnog dijela potencijala, koja je u Lennard-Jonesovom potencijalu 12, utječe na karakteristične veličine sustava; energiju i srednju kvadratnu udaljenost. U radu je pokazan univerzalni odnos ovih veličina za različite sustave kvantnih dimera. Schrödingerova jednadžba za ove kvantne sustave nije rješiva analitički pa njenom rješavanju pristupamo numeričkim metodama pogađanja i usklađivanja (shoot and match) te Numerovom metodom. Osim samog iznošenja rezultata priloženo je i detaljno obrazloženje ovih metoda, programskog koda i rješavanja jednadžbe te skaliranja fizičkih veličina radi usporedbe različitih sustava.
Abstract (english)
The most popular two-particle potential model, the Lennard-Jones (12-6) potential, consists of a short-range repulsive part and a long-range attractive part. This thesis examines how the exponent of the short-range part of the potential, which is 12 in the Lennard-Jones potential, affects the characteristic quantities of the system, such as energy and the mean square distance. The study demonstrates the universal relationship of these quantities for different quantum dimer systems. The Schrödinger equation for these quantum systems cannot be solved analytically, so we approach its solution using numerical methods such as the shoot and match method and the Numerov method. In addition to presenting the results, a detailed explanation of these methods, the program code, and the solution of the equation is provided, as well as the scaling of physical quantities for comparing different systems.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:085509
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 on2024-09-23 10:41:00