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Solid-state physics studies how macroscopic properties of solids (mechanical, electrical, optical, etc.) result from their microscopic structure. It usually deals with the scale where quantum properties of the particles are substantial.
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Orthogonality of single-particle wavefunctions in Slater determinant
No, it's not necessary but if the spin-orbitals aren't orthogonal it's much more complicated to compute matrix elements of operators between such Slater determinants (Slater-Condon rules). Valence-bon …