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The Klein-Gordon Equation and Pionic Atoms
KTH, School of Engineering Sciences (SCI), Theoretical Physics.
KTH, School of Engineering Sciences (SCI), Theoretical Physics.
2014 (English)Independent thesis Basic level (degree of Bachelor), 10 HE creditsStudent thesis
Abstract [en]

This bachelor thesis introduces the Klein-Gordon equation and pionic atoms through

a historical review. It discusses properties of the equation and its continuity equation

based on a comparison with the Schrödinger equation and its continuity equation. The

conclusion that the Klein-Gordon equation is a relativistic extension of the Schrödinger

equation for spin-0 particles is drawn. This makes it possible to derive a Klein-Gordon

equation and Coulomb potential based model for pionic atoms. The transition energies

and the charge density for a pionic atom are derived. The model and a Schrödinger equation

model are used to draw conclusions on the differences between regular and pionic

atoms. Numerical predictions of the models are compared to experimental data and the

accuracy of the models is discussed. Properties of the pionic atom are discussed based

on the radial charge density.

Abstract [sv]

I detta kandidatexamensarbete introduceras Klein-Gordonekvationen och pionska atomer

via en historisk genomgång. Egenskaper hos ekvationen och dess kontinuitetsekvation

diskuteras baserat på en jämförelse med Schrödingerekvationen och dess kontinuitetsekvation.

Vi drar slutsatsen att Klein-Gordonekvationen är en relativistisk utvidgning

av Schrödingerekvationen för spin-0-partiklar. Detta möjliggör härledningen av en

modell för pionska atomer baserad på Klein-Gordonekvationen och Coulombpotentialen.

Övergångsenergierna och laddningstätheten härleds för en pionsk atom. Modellen används

tillsammans med en modell baserad på Schrödingerekvationen för att dra slutsatser

om skillnaderna mellan vanliga och pionska atomer. Numeriska förutsägelser från

modellerna jämförs med experimentella data och modellernas giltighet diskuteras. Egenskaper

hos pionska atomer diskuteras baserat på den radiella laddningstätheten.

Place, publisher, year, edition, pages
2014. , 28 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-145862OAI: oai:DiVA.org:kth-145862DiVA: diva2:720773
Supervisors
Available from: 2014-06-02 Created: 2014-06-02 Last updated: 2014-06-02Bibliographically approved

Open Access in DiVA

Kandidatexamensarbete Anna Nolinder, Elin Sandberg(287 kB)681 downloads
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