# Spin and wavefunction of Excitons

My Bachelor thesis is all around Excitons (specifially transitions between excitons of different energies). During my work I often had trouble with the spin and the wavefunction of them. Is there maybe some good (free) literature about the theory of excitons ? I found some books in the internet but they werent for free. And my university hasnone.

1) I read about "heavy holes" that can have spin of +-3/2. How can these be created ? And for example a 3/2 hole bonds with a 1/2 electron. Then the Exciton has spin 2. How would the wave function of this look like ? I know that in 3D the wavefunctions of hydrogen can be used for the wavefunctions of the exciton. And thats why I think if there is a spin 2 Exciton, it can only exist at higher Energies E(n) (since a hydrogen atom only can have spin 2 when it's n is 3 or higher). But on the other side, my professor now wrote me that there is also a $$|2,1,-2\rangle$$ (n=2,l=1,m=-2)

2) $$|3,2,2\rangle \Rightarrow |1,0,0\rangle + 2 photons$$ is this possible ?
Or is just the following possible: $$|3,2,2\rangle \Rightarrow |2,1,1\rangle + 1 photon \Rightarrow (|1,0,0\rangle + 1 photon) + 1 photon$$

Or in Words: If now there is an Exciton with spin 2 and n=3. Can it for example jump directly to n=1 with the emission of 2 photons (afterwards it will be an exciton with spin 0)? Or can it only First jump to n=1 with the emission of 1 photon (then it will be an Exciton with spin 1) and then to n=0 with the emission of another Photon (then it will be an Exciton with spin 0)

• This answer is probably relevant, although the question is certainly not a duplicate. I particularly recommend the linked book by Knox - he demonstrates rather convincingly that excitons are many-particle excitation and that their spin is poorly defined. Jun 30, 2022 at 14:55