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master's thesis
Analiza vezanih kvantnih harmonijskih oscilatora difuzijskim algoritmom
Split: University of Split, University of Split, Faculty of science, 2022. urn:nbn:hr:166:034054
Volarević, Domagoj
University of Split
Faculty of Science
Department of Physics

Institutional repository: Repository of Faculty of Science

Cite this document

Volarević, D. (2022). Analiza vezanih kvantnih harmonijskih oscilatora difuzijskim algoritmom (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:034054

Volarević, Domagoj. "Analiza vezanih kvantnih harmonijskih oscilatora difuzijskim algoritmom." Master's thesis, University of Split, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:166:034054

Volarević, Domagoj. "Analiza vezanih kvantnih harmonijskih oscilatora difuzijskim algoritmom." Master's thesis, University of Split, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:166:034054

Volarević, D. (2022). 'Analiza vezanih kvantnih harmonijskih oscilatora difuzijskim algoritmom', Master's thesis, University of Split, Faculty of Science, accessed 29 December 2024, https://urn.nsk.hr/urn:nbn:hr:166:034054

Volarević D. Analiza vezanih kvantnih harmonijskih oscilatora difuzijskim algoritmom [Master's thesis]. Split: University of Split, Faculty of Science; 2022 [cited 2024 December 29] Available at: https://urn.nsk.hr/urn:nbn:hr:166:034054

D. Volarević, "Analiza vezanih kvantnih harmonijskih oscilatora difuzijskim algoritmom", Master's thesis, University of Split, Faculty of Science, Split, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:166:034054

Metadata
TitleAnaliza vezanih kvantnih harmonijskih oscilatora difuzijskim algoritmom
Title (english)Analyzing coupled quantum harmonic oscillators using the diffusion algorithm
AuthorDomagoj Volarević
MentorŽeljana Bonačić Lošić (mentor)
Committee memberŽeljana Bonačić Lošić (predsjednik povjerenstva)
Committee memberPetar Stipanović (član povjerenstva)
Committee memberIvana Weber (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Physics)
Split
Defense date and country2022-09-16, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
U ovom radu analizira se problem vezanih kvantnih harmonijskih oscilatora, koji zahtijeva rješavanje Schrödingerove jednadžbe za određeni potencijal. Rješenja se dobivaju pomoću difuzijskog algoritma koji se temelji na propagaciji sustava u imaginarnom vremenu, dok se ortonormalizacija provodi algoritmom podprostorne ortogonalizacije. Proučena je preciznost i učinkovitost raznih dekompozicija evolucijskog operatora na jednostavnim primjerima koje je moguće analitički riješiti. Osim toga, proučeno je i uklanjanje degeneracije na višedimenzionalnim sustavima, koje je očekivano iz teorije računa smetnje. Praktična primjena ovog sustava može se pronaći u optici, u problemu širenja svjetla u nehomogenom mediju, te za promatranje čestica u proizvoljnom magnetnom polju. Prednost ovog pristupa nad dosadašnjim numeričkim metodama je u velikoj preciznosti i bržem vremenu simulacije, što omogućava račun za jako velik broj čestica i energijskih stanja.
Abstract (english)
This thesis focuses on analyzing coupled quantum harmonic oscillators. This problem can be solved using the Schrödinger equation for a given potential. The solution is produced by the diffusion algorithm which is based on imaginary time propagation. The orthonormalization is done using the subspace orthonormalization algorithm. Simpler models which can be solved analytically are used to explore the precision and efficiency of different decompositions of the evolution operator. As expected from the perturbation theory, the breaking of degeneracy of multidimensional systems is also shown. The practical use of this model can be found in optics, in the form of light propagation in inhomogeneous media, and can also be used to study particles in an arbitrary magnetic field. The main advantage of this method is excellent precision and very short simulation time, which makes calculations for a great number of particles and energy states possible.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:034054
Study programmeTitle: Physics; specializations in: major in teaching, major in Astrophysics, major in Biophysics, major in Enviromental physics, major in Computational physics, major in Astrophysics and physics of elemental particles
Course: major in Computational physics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-11-03 13:26:48