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05_04_29 - 168 The radial part of the wave function&2 L(r =...

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[email protected] 168 The radial part of the wave function 04/29/2005 7KH±HIIHFWLYH±UDGLDO±SRWHQWLDO² 2 2 2 2 2 2 0 ( 1) 1 1 1 4 2 2 [ ] ( ) l l e nl nl nl r m m r r r R rR E R πε + - - - = 2 2 2 1 1 2 ˆ ˆ ( ) ( , , ) ( ) ( , , ) ( , , ) r m r V r r p L r E r ϑ ϕ ϑ ϕ ϑ ϕ Φ + + Φ = Φ & 2 2 2 2 1 ˆ ( , , ) ( ) ( , ) , ( ) nl r r r r R r f p r ϑ ϕ ϑ ϕ Φ = Φ = - Φ ! ( ) eff V r ( ) V r 2 2 ( 1) 1 2 l l m r + E r ] [ ] [ ] [ 2 2 0 0 2 0 2 0 0 0 2 2 2 0 2 ) 1 ( 2 1 ) / ( ) 1 ( 2 8 / 2 8 ) 1 ( 2 4 ξ ξ πε πε πε + + + - - = - - = - - = l l a r l l a me a r a e r l l m r e eff E V
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[email protected] 169 Energy and angular momentum 04/29/2005 ( ) eff V r E r 2U³± YLVXDO±UHDVRQLQJ ² (±KDV±WR±EH±ELJJHU±WKDQ 9 2 2 3 min min 2 1 ( 1) 2 ( 1) 2 min 2 1 1 min ( 1) 2 0 ( 1) ( 1) l l eff l l eff E l l E n V V l l V l l n ξ ξ ξ ξ ξ + + + = - + = - = = + - = = + 1 l n - min V WXUQV±RXW±WR±EH±LQGHSHQGHQW±RI±O´ 0 0 2 2 2 8 1 1 1 , a e n n n E E E πε - = = } 1 , , 0 { - n l ±
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[email protected] 170 The complete wave function 04/29/2005
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