固体电子论前编.PDF

Quantum Theory of Solid-State Electron Systems: Part I ö d i ϕ (t) = H (t) ϕ (t) dt Hamiltonian H ( ) ⎛ ε ⎞ ϕ t = exp⎝ i t⎠ ϕ H ϕ = ε ϕ H ν = ε ν ν ν µ = δ νµ A A = ν A ν ν 1 ν ∑ ν ν = 1 ν ϕ = ∑ ν ν ⋅ ϕ ν = ∑ a ⋅ ν , a ≡ ν ϕ ν ν ν νFourier Hamiltonian H A A = ϕ A ϕ = ∑ ϕ ν ν A µ µ ϕ νµ * = ∑ a a ν A µ ν µ νµ Dirac Schrödinger ϕ (r ) ⇔ r ν , ϕ * (r) ⇔ r ν + ≡ ν r ν ν ( ) r r = δ r − r , ∫ r r dr = 1 2 ε ϕ (r) = ε r ν ν ν ν = r H ν = ∫ r H r r ν dr ( ) ( ) = r H r r ν ⇒ H r ϕν r * ( ) ( ) ( ) A ν = ∫ϕν r A r ϕν r dr * ( ) ( ) ( )