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05_05_06 - [email protected] 174 The periodic...

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Unformatted text preview: [email protected] 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 [email protected] 175 The total angular momentum 05/06/2005 7KH WRWDO DQJXODU PRPHQWXP - KDV DQJXODU PRPHQWXP FRPPXWDWRUV The Schrödinger equation ˆ ˆ ˆ [ , ] i j ijk k J J i J ε = ! DQG WKHUHIRUH KDV HLJHQYDOXHV 2 ( 1) j j + ! 2 ˆ J & :KHUH DJDLQ D VLPXOWDQHRXV HLJHQIXQFWLRQ RI / ZDV FKRVHQ 2 2 2 2 2 ˆ ˆ ˆ ˆ ˆ [ , ] [ , 2 ] i i L J L L L S S = + + = & & & & & 2QH FDQ DGGLWLRQDOO\ FKRRVH VLPXOWDQHRXV HLJHQIXQFWLRQV RI - VLQFH This leads to a one dimensional Schrödinger equation were the set of eigenfunctions depends on l and j: ( ) , nl j nl j R r E E Φ ∝ = Spin orbit coupling S L J S J L p r V S L S L L p S...
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05_05_06 - [email protected] 174 The periodic...

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