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I think I understood the density of states, but I didn't understand the joint DOS. What is the main difference? What is the exact definition of the joint DOS?

When do we use the joint DOS and when do we simple use the DOS?

edit: Let's consider we are in a semiconductor system, for simplicity GaAs

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    $\begingroup$ You use the joint density of states when you have a process going from one state to another. For example, optical excitation of an electron from the valence band to the conduction band - you need to account for how many electrons are available, and whether there are any states that you can excite them into. If the photon energy is too low, there will be no accessible states. $\endgroup$
    – Jon Custer
    Commented Mar 25, 2020 at 14:39
  • $\begingroup$ Could you please tell us, which system you are considering. E.g. if you consider the possible states of two electrons in an atom, they have to obey Pauli's exclusion principle. Hence, the joint DOS is not equal to the product of the single electron DOS. $\endgroup$
    – NotMe
    Commented Mar 25, 2020 at 17:18
  • $\begingroup$ @Semoi: Does it mean if we are not in atomic physics with dipole transitions, then the joint DOS is the product of the initial x final DOS? $\endgroup$
    – cerv21
    Commented Mar 25, 2020 at 22:53

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