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master's thesis
Matematičke formulacije principa neodređenosti
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:705333
Radulović, Marko
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Radulović, M. (2014). Matematičke formulacije principa neodređenosti (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:705333

Radulović, Marko. "Matematičke formulacije principa neodređenosti." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:705333

Radulović, Marko. "Matematičke formulacije principa neodređenosti." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:705333

Radulović, M. (2014). 'Matematičke formulacije principa neodređenosti', Master's thesis, University of Zagreb, Faculty of Science, accessed 01 January 2025, https://urn.nsk.hr/urn:nbn:hr:217:705333

Radulović M. Matematičke formulacije principa neodređenosti [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2025 January 01] Available at: https://urn.nsk.hr/urn:nbn:hr:217:705333

M. Radulović, "Matematičke formulacije principa neodređenosti", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:705333

Metadata
TitleMatematičke formulacije principa neodređenosti
AuthorMarko Radulović
MentorVjekoslav Kovač (mentor)
Committee memberVjekoslav Kovač (predsjednik povjerenstva)
Committee memberIgor Pažanin (član povjerenstva)
Committee memberMarko Tadić (član povjerenstva)
Committee memberZvonimir Tutek (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-09-23, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Princip neodređenosti prvi puta je formulirao W. Heisenberg 1927. godine čime je pokazano da se određene fizikalne vrijednosti poput položaja čestice i momenta ili pak vremena i energije ne mogu proizvoljno precizno odrediti, što je značajno odudaralo od dotadašnjeg iskustva u fizici. Iste godine, Kennard pokazuje isti princip u punom matematičkom formalizmu, čime je motivirano proučavanje principa u raznim matematičkim kontekstima. Koristeći fundamentalne rezultate Fourierove analize te poštujući matematički formalizam kvantne mehanike, iznosimo razne formulacije principa neodređenosti. Sam princip promatramo za jednu funkciju – njegove kvalitativne, kvantitavne, operatorske te entropijske formulacije, potom za Gaborove i valićne sisteme funkcija te, naposljetku, općenito za konačne abelove grupe, te specifično za cikličke grupe prostog reda.
Abstract (english)
The uncertainty principle was first formulated by W. Heisenberg in the year 1927, which showed that certain physical values such as the position and the momentum of a particle, and also the time and the energy, cannot be specified with an arbitrary precision, something that was far from experiences in physics before the principle was discovered. In the same year, Kennard showed the same principle using a rigorous mathematical formalism, which has motivated further research of the principle in many different mathematical contexts. Using the fundamental results of Fourier analysis, and respecting the mathematical formalism of quantum mechanics, we present many different formulations of the uncertainty principle. We observe the principle for a single function – its qualitative, quantitative, operator and entropic formulations, for Gabor and wavelet systems of functions, and finally, generally for finite abelian groups, and more specifically for cyclic groups of prime order.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:705333
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-05 11:25:10