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? (b) Consider the following state, for n = 2: 2) = a |200) + 3|210), wherea, ß C. In this state the expectation value of the electric dipole momentoperator 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 leftoverterms are conjugate of each other as the expectation value of pe must bereal, 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, 200and 210, we find that, Pe = qr.π2πT11r9(200)/(210) - ² dr sin 8 de fa do (val (2-2) 6-1/2") (₁√ (2)-¹1/20 cm)e-r/2a)=4√a³πa4√a³πaJO0200210

As we can see that the two part of the expression are

Answered: (Pe) = a* (200|pe|210) + aß*…

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(Pe) = a* (200|pe|210) + aß* (200|pe|210)* = 2 Re {a* 3 (200|pe|210)