Elements of Rayleigh–Schroedinger Perturbation Theory - Methods of Molecular Quantum Mechanics - page 213

so that

cos

c 2
2 r

H 0 exp ð cr Þ r cos

½ u ¼ exp ð cr Þð 2c 1 Þ u ð 10 : 129 Þ

We then obtain for the integral:

" # exp ð 2cr Þ

ð

dxx 2 1

1

c 5
p

c 2
2 r 2

h 2p z j H 0 j 2p z i¼

drr 2

2 p ð 2c 1 Þ r

1 0

2
4

3
5 ¼

c 2
2

c 2
2

4 3 2

ð 2c Þ

4 3 2
ð 2c Þ

c
2 3 c 5

¼ ð 2c 1 Þ

4 5

ð 10 : 130 Þ

giving for the excitation energy

1

« ¼h 2p z j H 0 E 0 j 2p z i¼

2 ð c 2

c þ 1 Þ ð 10 : 131 Þ