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I need a book that explains the tight binding model in second quantization formalism. for example by telling the meaning of the eigenfunctions of kernel of Hamiltonian in $k$ space. also explains $2$ atom per site or $2$ orbitals per site (is there a difference?). Also there are some lecture notes explains this but, I don't trust them since they are lecture notes.

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  • $\begingroup$ -1. No research effort. What books have you found and rejected? What are the lecture notes? $\endgroup$ – sammy gerbil Dec 12 '16 at 21:40
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Mahan's "Many-Particle Physics" explains the tight-binding model in second quantization formalism at pages 20-26 of the third edition. You can find it here:

https://books.google.it/books?id=TFDUBwAAQBAJ

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  • $\begingroup$ Than you for your suggest but, it's a little bit brief. i want to learn the meaning of the eigenstates of kernel of second quantized hamiltonian in momentum space, it is a nxn matrix where n is number of bands. and eigen values of this matrix gives the energy of band but what does eignvectors give? and that book does not adress that question. $\endgroup$ – physshyp Dec 12 '16 at 14:55
  • $\begingroup$ @physshyp The eigenvector gives the wave function of electrons among the atoms/orbitals in the unit cell for that single-particle state. $\endgroup$ – Everett You Dec 12 '16 at 15:00

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