Physics for Semiconductors

In quantum mechanics, any quantum state ‘vector’ | i may be expanded as a linear superposition of the eigenvectors of any Hermitian operator | i = P n an|ni. This is the Expansion Principle of quantum mechanics. For most problems, the Hermitian operator of choice is the Hamiltonian operator Ĥ = (p̂/2m0) + V (r), but it need not be. We choose the Hamiltonian operator since there exist a few problems for which we know the set of exact eigenvectors [. . . , |n 1i, |ni, |n+ 1i, . . .]. These sets of eigenvectors are complete. We also discussed in chapter 2 that this choice of eigenstates are stationary, which makes life easier. We do not consider pathological functions here.