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    Why can we choose wavefunctions to be real?

    There are many cases, for simplicity, we choose the wavefunctions to be real. For example, in, there is "The electronic wave functions \chi_k\, will be taken to be real, which is possible when there are no magnetic or spin...
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    The motivation of k.p method and envelope function method?

    There are various kinds of approximation methods in band theory. In my opinion, Bloch theorem implies the existence of energy band. From nearly-free electron approximation or tight binding method, we can calculate the energy band. They can tell us the information of band gap and band width...
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    Why is OPW complete?

    Orthogonal plane waves can be used to expand Bloch waves. It is better than plane waves because it converges more quickly. However, I've got a problem. The completeness of plane waves is guaranteed by Fourier analysis. Why is OPW complete? It is orthogonal to core levels. But does it mean OPW is...
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    Some basic problems with energy band

    I am learning Ashcroft's Solid State Physics. In the Electrons in a Weak Periodic Potential, I got some problems. 1. Ashcroft mentioned in the footnote: The reader familiar with stationary perturbation theory may think that if there is no exact degeneracy, we can always make all level...
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    Symmetry in quantum mechanics

    I have several questions about symmetry in quantum mechanics. It is often said that the degeneracy is the dimension of irreducible representation. I can understand that if the Hamiltonian has a symmetric group G, then the state space with the same energy eigenvalue will carry a...