Hi, can someone help me with this problem?(adsbygoogle = window.adsbygoogle || []).push({});

A hydrogen atom is in the 2P state with n=2, l=1, m=1. It emits a photon and makes a transition to the 1S state (n=1, l=0, m=0).

The question is what is the probability distribution of the direction [tex](\theta , \phi)[/tex] of the emitted photon?

The answer is:

[tex]P(\theta , \phi)=\frac{3}{16\pi} (1+(cos(\theta)^{2})[/tex]

Thanks!!

The solution is not very clear but the following facts may be helpful. Can someone please explain this problem clearly to me? I am having a very difficult time understanding this.

The electric field can be expressed in terms of creation and annihilation operators of photons in a box of volume V.

We know that the interaction is [tex]H_{I} = \vec{E} \cdot \vec{d} = -e \vec{E} \cdot \vec{r} [/tex] (d is electric dipole moment) so we know the matrix element of a photon is:

[tex]<i|H_{I}|f> = -e\sqrt{\frac{\hbar c k}{2 \epsilon_0 V}} <2P|\vec{\epsilon} \cdot \vec{r} | 1S>[/tex]

From here, I don't understand what to do. If you can find a similar problem worked out online that would be helpful as well.

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# Homework Help: Quantum mech question - hydrogen help?

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