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Unformatted text preview: Towards Electrons in Solids ) , ( ) , ( ) , ( 2 ) , ( 2 2 2 t x t x V t x x m t x t i + = - Review Schroedinger wave equation Arrived at the time independent version by solving for through separation of variables and taking V = V(x) only ) , ( t x ) ( ) ( ) , ( t T x t x = t i t E i e e t T ) / ( ) ( -- = = ) ( ) ( ) ( 2 ) ( 2 2 2 x x V x x m x E + =- Time independent wave equation Electrons about an atomic nucleus: Coulombic interaction ) , ( ) ( 4 2 f r V r Ze V o =- = ) ( ) ( ) ( ) , , ( = r R r Exact analytical solution for one electron n l m l Energy Angular momentum Electrons in Atoms Z n r n 2 Single electron atom or ion (arbitrary Z ) orbitals known exactly Multi-electron atoms : ( Z > 1) 2 2 6 . 13 n Z E n- = Hydrogen : Z = 1 1s, 2s, 2p, 3s, 3p Pauli exclusion principle only one electron with given set of quantum numbers cant all be in the lowest energy state; fill lowest first, then go up...
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This note was uploaded on 01/03/2012 for the course MS 115a taught by Professor List during the Fall '09 term at Caltech.
- Fall '09