[PDF] Meaning of Ueff



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Meaning of Ueff

Meaning of U

eff

Total wave function (Text 6.3-6.6)

22
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

U(r)2mrL

dtdrm21 energy Total

With 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 ]=0

3. 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 r

Total wave function (Text 6.3-6.6)

21-n
01-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

1

0 0

-1

1 0

1 -2

3 -1 9

2 0

1 2 n n 2 m

Total 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 22
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