Charmonium-hiukkasen energiatilojen määrittäminen Cornellin potentiaalin avulla

Tämän tutkielman tarkoituksena on tutkia charmonium-hiukkasen energiatiloja Cornellin potentiaalin avulla. Potentiaalin parametrit määritetään kokeellisesti mitattujen energiatilojen ja hajoamisleveyksien avulla. Hajoamisleveyksille käytetään QCD:n häiriöteorian antamia lausekkeita. Parametrien ratk...

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Main Author: Penttala, Jani
Other Authors: Matemaattis-luonnontieteellinen tiedekunta, Faculty of Sciences, Fysiikan laitos, Department of Physics, Jyväskylän yliopisto, University of Jyväskylä
Format: Bachelor's thesis
Language:fin
Published: 2018
Subjects:
Online Access: https://jyx.jyu.fi/handle/123456789/59126
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author Penttala, Jani
author2 Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Fysiikan laitos Department of Physics Jyväskylän yliopisto University of Jyväskylä
author_facet Penttala, Jani Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Fysiikan laitos Department of Physics Jyväskylän yliopisto University of Jyväskylä Penttala, Jani Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Fysiikan laitos Department of Physics Jyväskylän yliopisto University of Jyväskylä
author_sort Penttala, Jani
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description Tämän tutkielman tarkoituksena on tutkia charmonium-hiukkasen energiatiloja Cornellin potentiaalin avulla. Potentiaalin parametrit määritetään kokeellisesti mitattujen energiatilojen ja hajoamisleveyksien avulla. Hajoamisleveyksille käytetään QCD:n häiriöteorian antamia lausekkeita. Parametrien ratkaisemista varten kirjoitetaan charmoniumin Schrödingerin yhtälö dimensiottomasta muodossa, jolloin Schrödingerin yhtälön ratkaiseminen on mahdollista tehdä numeerisesti. Aaltofunktion ja ominaisenergioiden numeerisessa ratkaisemisessa käytetään MATLAB-ohjelmaa. Ratkaistuilla parametrien arvoilla on laskettu charmoniumin alimpien energiatilojen massoja, jotka yleisesti ottaen noudattavat mitattujen ja muiden teoreettisten mallien antamien massojen arvoja. Tämän perusteella Cornellin potentiaali toimii hyvin charmoniumin karkeana mallina, jonka avulla voidaan selittää mitattujen energiatilojen rakennetta. The purpose of this thesis is to examine the energy states of the charmonium particle using the Cornell potential. The potential contains unknown parameters which have to be determined in order to use the potential. This is done by using the measured energy states and decay widths. The decay widths are made coincide with the theoretical values calculated from formulas given by perturbative QCD. In order to solve for the parameters, the Schrödinger equation for the charmonium particle is written in a dimensionless form allowing a numerical solution of the Schrödinger equation. The corresponding wave function and the eigenenergies are solved numerically using a MATLAB program. The solved parameter values are then used to calculate the masses of the lowest energy states. These masses generally agree with the measured values and the values calculated from other theoretical models. Based on this, the Cornell potential works well as a rough model for charmonium and can be used to explain the structure of the measured energy states.
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Potentiaalin parametrit m\u00e4\u00e4ritet\u00e4\u00e4n kokeellisesti mitattujen\nenergiatilojen ja hajoamisleveyksien avulla. Hajoamisleveyksille k\u00e4ytet\u00e4\u00e4n\nQCD:n h\u00e4iri\u00f6teorian antamia lausekkeita. Parametrien ratkaisemista varten kirjoitetaan\ncharmoniumin Schr\u00f6dingerin yht\u00e4l\u00f6 dimensiottomasta muodossa, jolloin Schr\u00f6dingerin\nyht\u00e4l\u00f6n ratkaiseminen on mahdollista tehd\u00e4 numeerisesti. Aaltofunktion\nja ominaisenergioiden numeerisessa ratkaisemisessa k\u00e4ytet\u00e4\u00e4n MATLAB-ohjelmaa.\nRatkaistuilla parametrien arvoilla on laskettu charmoniumin alimpien energiatilojen\nmassoja, jotka yleisesti ottaen noudattavat mitattujen ja muiden teoreettisten\nmallien antamien massojen arvoja. T\u00e4m\u00e4n perusteella Cornellin potentiaali toimii\nhyvin charmoniumin karkeana mallina, jonka avulla voidaan selitt\u00e4\u00e4 mitattujen\nenergiatilojen rakennetta.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "The purpose of this thesis is to examine the energy states of the charmonium particle\nusing the Cornell potential. The potential contains unknown parameters which\nhave to be determined in order to use the potential. This is done by using the\nmeasured energy states and decay widths. The decay widths are made coincide\nwith the theoretical values calculated from formulas given by perturbative QCD.\nIn order to solve for the parameters, the Schr\u00f6dinger equation for the charmonium\nparticle is written in a dimensionless form allowing a numerical solution of the\nSchr\u00f6dinger equation. The corresponding wave function and the eigenenergies are\nsolved numerically using a MATLAB program. The solved parameter values are then\nused to calculate the masses of the lowest energy states. These masses generally agree\nwith the measured values and the values calculated from other theoretical models.\nBased on this, the Cornell potential works well as a rough model for charmonium\nand can be used to explain the structure of the measured energy states.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Riitta Pitk\u00e4nen (rpitkane@jyu.fi) on 2018-08-06T11:56:18Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2018-08-06T11:56:19Z (GMT). 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spellingShingle Penttala, Jani Charmonium-hiukkasen energiatilojen määrittäminen Cornellin potentiaalin avulla charmonium Cornellin potentiaali hajoamisleveys Fysiikka Physics 4021 hiukkasfysiikka
title Charmonium-hiukkasen energiatilojen määrittäminen Cornellin potentiaalin avulla
title_full Charmonium-hiukkasen energiatilojen määrittäminen Cornellin potentiaalin avulla
title_fullStr Charmonium-hiukkasen energiatilojen määrittäminen Cornellin potentiaalin avulla Charmonium-hiukkasen energiatilojen määrittäminen Cornellin potentiaalin avulla
title_full_unstemmed Charmonium-hiukkasen energiatilojen määrittäminen Cornellin potentiaalin avulla Charmonium-hiukkasen energiatilojen määrittäminen Cornellin potentiaalin avulla
title_short Charmonium-hiukkasen energiatilojen määrittäminen Cornellin potentiaalin avulla
title_sort charmonium hiukkasen energiatilojen määrittäminen cornellin potentiaalin avulla
title_txtP Charmonium-hiukkasen energiatilojen määrittäminen Cornellin potentiaalin avulla
topic charmonium Cornellin potentiaali hajoamisleveys Fysiikka Physics 4021 hiukkasfysiikka
topic_facet 4021 Cornellin potentiaali Fysiikka Physics charmonium hajoamisleveys hiukkasfysiikka
url https://jyx.jyu.fi/handle/123456789/59126 http://www.urn.fi/URN:NBN:fi:jyu-201808063740
work_keys_str_mv AT penttalajani charmoniumhiukkasenenergiatilojenmäärittäminencornellinpotentiaalinavulla