Explain why each of the following integrals must be 0 when the functions are hydrogen-like wavefunctions:
<2p1|Lz|3p-1> and <2p0|Lz|2p0>
Show that taking the lithium spin orbitals in a Slater determinant as 1sa,
1sb, and 1s(c1a+c2b) where c1 and c2 are constants gives a wavefunction that equals zero.
Tthe a and b are alpha and beta.
This problem also has the 2p0 but I thought the p orbital had -1 0 and 1.
The answer is in the attachment. Thanks!
<2p1|Lz|3p-1> = <R21 Y21| Lz | R31 Y2,-1>
= <R21 | R31> < Y21| Lz | Y2,-1>
= 0 < Y21| Lz | Y2,-1>
This solution provides a detailed break down of equations in order to show how an integral has to be zero according to wavefunctions.