05_05_04 - )LQHVWUXFWXUHVSOLWWLQJRI6RGLXPO OLQHPH9...

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Georg.Hoffstaetter@Cornell.edu 171 Wave functions with properties that resemble Bohr orbits 05/04/2005 2 1 max 0 1, n l n m l r a = - = ± = ( 29 ( 29 1 0 2 0 0 1 ( 1) 1 1, 1 2 2 2 2 1 2 2 max max ( , , ) ( ) ( , ) sin ( ) 4 | | 2 0 n a n a r n i n nn n n r n n n na r R r Y e r e r r r e nr r ϕ ϑϕ ϑ ρ π - - ± - - - ± - - - Φ = = Φ - = ( 29 1 1 2 0 1 1 2 3 [( 1) ] 1 2 ( , ) ( ) sin ( ) E E n n a n i n t r n i t E E group rot n n n x t x e e r e ϖ - - - - - Ψ = Φ = = - = ± , , 4 2 2 2 2 0 0 2 2 2 0 1 2 2 3 2 1 1 2 4 2(4 ) 2 2 2 1 1 8 2 2 2 2 , n n n n n n n n me e n r n E E E E n e m E E m E E m E v rot r m n n E mv v r πε - - - - - - - - = - = - = = = = = = 2 | | . const Φ =
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Georg.Hoffstaetter@Cornell.edu 172 Spin-Orbit coupling energy 05/04/2005 7 24 0 3 3 30 2 10 9.27 10 1 1 0 0 0 2 2 2 4 2 10 2 qv q z z B r r r mr r B I L m m m T μ π - - - = = = = IUDPH±D±PDJQHWLF±ILHOG±GXH±WR±WKH±FLUFOLQJ±SURWRQ³ $VVXPLQJ±WKH±FLUFXODU±PRWLRQ±RI±D±%RKU±DWRP² EXW±WKH±PDJQHWLF±PRPHQW±LV±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± ZLWK 2 z S = ± ! 2 q z B s B m g m = ± = = ! 2 g 23 19 24 1.810 1.6 10 9 10 2 0.1 J B T E B B T eV meV - - - = - = ± ≈ ± ⋅ = ± ≈ ± 2UGHU±RI±PDJQLWXGH±HVWLPDWH±RI±VSLQ´RUELW±FRXSOLQJ±µ ILQH±VWUXFWXUH RI±WKH±VSHFWUXP¶² 5HDOLW\² )LQH±VWUXFWXUH±VSOLWWLQJ±RI±+\GURJHQ±O ·±OLQH²±¸³¸¹PH9
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Unformatted text preview: )LQHVWUXFWXUHVSOLWWLQJRI6RGLXPO OLQHPH9 7KHHQHUJ\RIVWDWHVZLWK O GRQRWFKDQJHGXHWRVSLQRUELWFRXSOLQJ VLQFHQRPDJQHWLFILHOGLVSURGXFHGIRUO Georg.Hoffstaetter@Cornell.edu 173 Hydrogen-like systems 05/04/2005 2 n E Z (QHUJ\OHYHOVRI$ONDOLDWRPVYHUVXV+\GURJHQ +LJKO\LRQL]HGDWRPVZLWKRQO\RQHHOHFWURQOHIW (QHUJ\OHYHOVRILQQHUPRVWHOHFWURQVZKLFKH[SHULHQFHD QHDUO\XQVKLHOGHGSRWHQWLDO7KHVHOLQHVEHFRPHYLVLEOH ZKHQDLQQHUPRVWHOHFWURQ.HOHFWURQKDVEHHQH[SHOOHG $ONDOLPHWDOVZKLFKKDYHDVLQJOHHOHFWURQLQWKHRXWHUVKHOO...
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05_05_04 - )LQHVWUXFWXUHVSOLWWLQJRI6RGLXPO OLQHPH9...

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