05_05_06 - Georg.Hoffstaetter@Cornell.edu 174 The periodic...

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Unformatted text preview: Georg.Hoffstaetter@Cornell.edu 174 The periodic table 05/06/2005 )LOO SDWWHUQ RI RXWHUPRVW HOHFWURQV Q ZLWK O Q ZLWK O WKHQ ZLWK O Q ZLWK O WKHQ ZLWK O EXW WKHQ QRW ZLWK O 6LQFH WKH Q O VWDWHV KDYH D SUREDELOLW\ FORVH WR WKH FRUH DQG WKHLU HQHUJ\ LV ORZHUHG l = 1 l = n 2 l = 3 l = l = n 3 4 4 n = 5 n = LVFRYHUHG Georg.Hoffstaetter@Cornell.edu 175 The total angular momentum 05/06/2005 7KH WRWDO DQJXODU PRPHQWXP - KDV DQJXODU PRPHQWXP FRPPXWDWRUV The Schrdinger equation [ , ] i j ijk k J J i J = ! DQG WKHUHIRUH KDV HLJHQYDOXHV 2 ( 1) j j + ! 2 J & :KHUH DJDLQ D VLPXOWDQHRXV HLJHQIXQFWLRQ RI / ZDV FKRVHQ 2 2 2 2 2 [ , ] [ , 2 ] i i L J L L L S S = + + = & & & & & 2QH FDQ DGGLWLRQDOO\ FKRRVH VLPXOWDQHRXV HLJHQIXQFWLRQV RI - VLQFH This leads to a one dimensional Schrdinger equation were the set of eigenfunctions depends on l and j: ( ) , nl j nl j R r E E = Spin orbit coupling S L J S J L p r V S L S L L p S...
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This note was uploaded on 09/28/2008 for the course PHYS 316 taught by Professor Hoffstaetter during the Spring '05 term at Cornell University (Engineering School).

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05_05_06 - Georg.Hoffstaetter@Cornell.edu 174 The periodic...

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