(Pe) = a* (200|pe|210) + aß* (200|pe|210)* = 2 Re {a* 3 (200|pe|210)
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I wrote a question mark where I'm confused. how does this step equal the last step? Why are they only taking the real part?
Transcribed Image Text:(b) Consider the following state, for n = 2: 2) = a |200) + 3|210), where
a, ß C. In this state the expectation value of the electric dipole moment
operator of the electron is
(pe) = (2|pe|2)
= |a|² (200|pe|200) + a* 3 (200|pe|210) + aß* (210|pe|200) + 131² (210|pe|210),
and since the first and fourth terms vanish by the virtue of Laporte's rule
(l+l' is even), we have
(Pe) = a* (200|pe|210) + aß* (210|pe|200) 0,
l' + l=1 (odd),
which is, according to Laporte's rule, not necessarily vanishing. The leftover
terms are conjugate of each other as the expectation value of pe must be
real, and therefore we can write
(Pe) = a* (200|pe|210) + aß* (200|pe|210)*
{a* B (200|pe|210) }
= 2 Re
= 2q Re{a*/3 (200|F|210) },
Restoring the explicit mathematical representation of the two states, 200
and 210, we find that
, Pe = qr.
π
2πT
1
1
r
9
(200)/(210) - ² dr sin 8 de fa do (val (2-2) 6-1/2") (₁√ (2)-¹1/20 cm)
e-r/2a)
=
4√a³π
a
4√a³π
a
JO
0
200
210
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