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222
2m r L 2m r (rp) 2 m pKE r 22
222
2m r L 2m r (rp) 2 m pKE 2 dtdrm21 KE eff U22 2
01-n 01-n 0 n n1)n-n( n
2 2 2 2 2 2 22
33
3 3 3 3 3 3 33
3 3 3 3 n=4 n=5 Why?1).2(2 are hereactually tbut columns, 12 have should Eachquotesdbs_dbs2.pdfusesText_3
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Meaning of U
effTotal wave function (Text 6.3-6.6)
22222
2m r L 2m r (rp) 2 m pKE r 22
222
2m r L 2m r (rp) 2 m pKE 2 dtdrm21 KE eff U22 2
U(r)2mrL
dtdrm21 energy TotalWith U
eff , the equation of motion can be reduced to one dimensional along r.Total wave function (Text 6.3-6.6)
1. E n , , and are simultaneous eigenvalues of H, L 2 , and L z 2. L 2 , and L z commute with H: [H, L 2 ]=0 and [H, L z ]=03. Measurements of H, L
2 , and L z will not affect each other.4. The solution is an eigenfunction
of H, L 2 , and L z simultaneously. )1( m ),(r)Y(R ),,( m n rTotal wave function (Text 6.3-6.6)
21-n01-n 01-n 0 n n1)n-n( n
2n)]1n(0[2 12 )12(n of Degeneracystates. degenerate called are Theseenergy. same thehave states 1)1)(2-(n theseAllies)possibilit 1(2 ,1 ...., 0, 1,...,- ,- mies)possibilit 1-(n 1-n 2,..., 1,
0,n, same For the
Total wave function (Text 6.3-6.6)
n degeneracy1 0 0 1
0 0
2 -1 4
1 0
10 0
-11 0
1 -23 -1 9
2 0
1 2 n n 2 mTotal wave function (Text 6.3-6.6)
We have special way to name orbital according to
the value of :The s-orbital is always spherical in shape.
Electron is a fermionNo two electron can
occupy the same state.As you add more electrons to an atom, these
electrons have to occupy higher and higher energy states.3 2 1 0 f d p s :name
Total wave function (Text 6.3-6.6)
n=1 n=2 n=3 n=4 n=5 n=6 n=7 01 01 1 1 1 1 222 2 2 2 2 2 22
33
3 3 3 3 3 3 33
3 3 3 3 n=4 n=5 Why?1).2(2 are hereactually tbut columns, 12 have should Eachquotesdbs_dbs2.pdfusesText_3