Transcription of Quantum Mechanics: The Hydrogen Atom
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Quantum Mechanics: The Hydrogen Atom
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).Her e,we have notplacedthecon-straint of a constant distancesepartingthemassesof therigidrotor(referto lastlecture);furthermore,we willkeepin theformulationthepotentialV(r; ; ) ,in sphericalpolarcoordinates,^H(r; ; ) (r; ; ) =E (r; ; )becomes:" h22 1r2@@r r2@@r +1r2sin @@ sin @@ +1r2sin2 @2@ 2!
energies associated with transsitions from the various energy lev-els of the hydrogen atom. The relation, simple enough as it is, turns out to accurately predict the spectral lines. The equation relating the wavelength (and thus energy via E= h ) associated with a transition from a state n1 to another tate nis given by: 1 = RRydberg 1 n2 1 1 n2
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