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Example:Energy states of a Lit ion. En R=13.6eV n E 0 3s 3印 3d Eis=-9R E2s.p=-(9/4)R 2s 2p E3s=-R 2.2.3 the azimuthal quantum number,l The operator of angular momentum M=M?+Mg+好 M.ih(sino- a +cot0cos 0 M=-ih(y 0 2 dy aφ a M,=-ih(= =-i(cos -一X cotesin Ox 0z a0 8o a a M.=-ih(x点-y M.=-ih- g 中 M2=-h 1 a a 1 o2 sin)+ sine 00 a0 sin20 002 1 a (sin() 1 aΦ(0) =-B Angular part Θ(0)sin0a0 a0 Φ(p)sin20ap22 n 2 Z E R n = − R = 13.6 eV Example: Energy states of a Li+ ion. E1s= - 9R E2s,sp= - (9/4)R E3s= - R ( ) ( ) ˆ ( ) ˆ ˆ ˆ ˆ ˆ 2 2 2 2 x y y M i x z x x M i z y z z M i y M M M M z y x x y z ∂ ∂ − ∂ ∂ = − ∂ ∂ − ∂ ∂ = − ∂ ∂ − ∂ ∂ = − = + + h h h The operator of angular momentum φ φ θ φ θ φ φ θ φ θ φ ∂ ∂ = − ∂ ∂ − ∂ ∂ = − ∂ ∂ + ∂ ∂ = ∧ ∧ ∧ h h h M i M i M i z y x (cos cot sin ) (sin cot cos ) ] sin 1 (sin ) sin 1 [ 2 2 2 2 2 θ θ φ θ θ θ ∂ ∂ + ∂ ∂ ∂ ∂ = − ∧ M h 2.2.3 the azimuthal quantum number, l β φ φ θ φ θ θ θ θ θ θ = − ∂ ∂ Φ Φ + ∂ ∂Θ ∂ ∂ Θ 2 2 2 ( ) ( )sin 1 ) ( ) (sin ( )sin 1 f Angular part
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