- #1

FrostInMyTeeth

- 1

- 0

_{fi}

^{4}e

^{2}/c

^{3}|< f | r | i >|

^{2}.

If we take the the | 2 1 1 > → | 1 0 0 > transition for example, we must compute the following integral :

< f | r | i > = C

_{1}∫∫∫ e

^{-r/a}r sin(θ) e

^{i*Φ}* e

^{-r/2a}sin(theta) r

^{2}sin(θ)dr dθ dΦ

, r = [ 0→ ∞], θ = [0 → pi], Φ = [0 → 2π]

Which can be separated in three integrals (depending on r, θ and Φ respectively). The integral in Φ is

I

_{Φ}= ∫ e

^{i*Φ}dΦ = 0

, Φ = [0 → 2π]

Which means that < f | r | i > = 0 and that the transition is not allowed. However in the literature (and logically), this transition is allowed.

I'm not quite sure if it's a comprehension issue or a simple computation error.

Thank you !