Transcription of Quantum Mechanics: The Hydrogen Atom
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QuantumMechanics:TheHydrogenAtom12thApri l2008I. TheHydrogenAtomIn thisnextsection,we willtietogethertheelements of thelastseveralsectionsto arrive at a completedescriptionof thede nitionof ,taken as a completebasis,we willbe abletoconstructapproximationsto morecomplexwave ,theworkof thelastfewlectureshasfundamentallybeenam iedat establishinga foundationformorecomplexproblemsin termsofexactsolutionsforsmaller, TheRadialFunctionWe willstartby reiteratingtheSchrodingerequationin 3 Dsphericalcoordi-natesas (referto any standardtextto getthetransformationfromCartesianto sphericalcoordinatereferencesystems).
ao = 2 oh 2 ˇ e2 The Radial eigenfunctions are: Rnl(r) = (n l 1)! 2n[(n+l)!]3 #1 2 2Z nao l+3 2 rle Zr nao L2l+1 n+l 2Zr nao The L2l+1 n+l 2Zr nao are …
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