Post on 01-Mar-2021
Mecânica Quântica II
Aula 5
Teoria de Perturbação: Caso degenerado múltiplo
Ref.: Griffiths, Int. Q.M., 2nd ed.
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)(2
1)( ixix ee
ixsen
)(2
1)( ixix ee
ixsen )2(
4
1)( 222 ixix eexsen ;
)(2
1)( ixix ee
ixsen )2(
4
1)( 222 ixix eexsen
dxeedxxsen ixix )2(4
1)( 222
;
)(2
1)( ixix ee
ixsen )2(
4
1)( 222 ixix eexsen
dxeedxxsen ixix )2(4
1)( 222
dxeedxxsen ixix
aa
)2(4
1)( 22
2/
0
2
2/
0
;
)(2
1)( ixix ee
ixsen )2(
4
1)( 222 ixix eexsen
dxeedxxsen ixix )2(4
1)( 222
dxeedxxsen ixix
aa
)2(4
1)( 22
2/
0
2
2/
0
4)(2
2/
0
adxxsen
a
;
)(2
1)( ixix ee
ixsen )2(
4
1)( 222 ixix eexsen
dxeedxxsen ixix )2(4
1)( 222
dxeedxxsen ixix
aa
)2(4
1)( 22
2/
0
2
2/
0
4)(2
2/
0
adxxsen
a
2)(2
0
adxxsen
a
;
;
4/a
4/a 4/a
4/a 4/a 2/a
4/a 4/a 2/a
4/a 4/a 2/a
mndxnxsenmxsen ,
02
)()(
)2
()(a
xsen
a
xsen
))((
4
1 /2/2// axiaxiaxiaxi eeee
)(4
1 //3/3/ axiaxiaxiaxi eeee
)3
cos(2
1)cos(
2
1
a
x
a
x
dxa
xsen
a
xsen
a
)2
()(
2/
0
dx
a
x
a
xa
)3
cos()cos(2
12/
0
2/
0
2/
0)
3(
3)(
2
1 aa
a
xsen
a
a
xsen
a
3
2
32
1 aaa