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The Phase-Integral Method, The Bohr-Sommerfeld Condition and The Restricted Soap Bubble: with a proposition concerning the associated Legendre equation
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
2011 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

After giving a brief background on the subject we introduce in section two the Phase-Integral Method of Fröman & Fröman in terms of the platform function of Yngve and Thidé. In section three we derive a different form of the radial Bohr-Sommerfeld condition in terms of the apsidal angle of the corresponding classical motion. Using the derived expression, we then show how easily one can calculate the exact energy eigenvalues of the hydrogen atom and the isotropic three-dimensional harmonic oscillator, we also derive an expression for higher order quantization condition. In section four we derive an expression for the angular frequencies of a restricted (0≤φ≤β) soap bubble and also give a proposition concerning the parameters l and m of the associated Legendre differential equation.

Abstract [sv]

Vi använder Fröman & Frömans Fas-Integral Metod tillsammans med Yngve & Thidés plattformfunktion för att härleda kvantiseringsvilkoret för högre ordningar. I sektion tre skriver vi Bohr-Sommerfelds kvantiseringsvillkor på ett annorlunda sätt med hjälp av den så kallade apsidvinkeln (definierad i samma sektion) för motsvarande klassiska rörelse, vi visar också hur mycket detta underlättar beräkningar av energiegenvärden för väteatomen och den isotropa tredimensionella harmoniska oscillatorn. I sektion fyra tittar vi på en såpbubbla begränsad till området 0≤φ≤β för vilket vi härleder ett uttryck för dess (vinkel)egenfrekvenser. Här ger vi också en proposition angående parametrarna l och m tillhörande den associerade Legendreekvationen.

Place, publisher, year, edition, pages
2011. , 26 p.
Series
FYSAST
Keyword [en]
Bohr-Sommerfeld quantization condition, phase-integral method, hydrogen atom energy levels, isotropic harmonic oscillator energy levels, theorem concerning parameters of the associated Legendre equation, apsidal angle, apsidal angle in semi-classical theory, WKB method, JWKB method, Old quantum mechanics, old quantum theory, Langer modification, half-integral quantization condition, Platform function, platform function of Yngve and Thidé, Fröman & Fröman theory, Fröman Fröman method
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:uu:diva-169572OAI: oai:DiVA.org:uu-169572DiVA: diva2:507275
Educational program
Bachelor Programme in Physics
Uppsok
Physics, Chemistry, Mathematics
Supervisors
Examiners
Available from: 2012-03-13 Created: 2012-03-02 Last updated: 2014-06-16Bibliographically approved

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