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Homework Statement
One way to establish which transitions are forbidden is to compute the expectation value of the electron’s position vector r using wave functions for both the initial and final states in the transition. That is, compute ∫ΨfrΨidτ where τ represents an integral over all space, and Ψf and Ψi are the final and initial states. If the value of the integral is zero, then the transition is forbidden.
Use this procedure to show that a transition from a L=1, mL=0 to a L=0 state is allowed.
Homework Equations
∫ΨfrΨidτ
R21(r)=Are^(-r/2a), A=1/(a^(5/2)2√6)
Y10(θ,φ)=1/2√(3/π)cosθ
The Attempt at a Solution
Just plug in values and solve. Easy!
But wait, I don't know what ψf is. The first state is the 2p state so I can find it's wave equation but the L=0 state has no other given quantum numbers.
I know that n>0, L<n and |mL|≤L so from what is given, the final state is n>0, L=0 and mL≤0.
So what do I do about the value of n and mL? How do I find the wave equation for the final state?
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