If we apply the time-independent Schrödinger equation to the Bloch wave function we obtain H ^ ^ k u k ( r ) = [ ℏ ℏ 2 2 m ( − − i ∇ ∇ + k ) 2 + U ( r ) ] u k ( r ) = ε ε k u k ( r ) with boundary conditions u k ( r ) = u k ( r + R ) Given this is defined in a finite volume we expect an infinite family of eigenvalues; here k is a parameter of the Hamiltonian and therefore we arrive at a "continuous family" of eigenvalues ε ε n ( k ) dependent on the continuous parameter k and thus at the basic concept of an electronic band structure.