The low-lying states for a one-dimensional potential consisting of N identical wells are considered,
assuming that the wells are parabolic around the minima. The N localized approximate eigenfunctions,
each of which matches an eigenfunction of the simple harmonic oscillator in one of the wells, are
constructed, relying on the WKB approximation. Diagonalizing the Hamiltonian in the subspace spanned
by the approximate eigenfunctions, a formula for the energy eigenvalues is obtained. The present
work will be useful for introducing Bloch wave functions in a periodic potential to undergraduate
and graduate students. It is shown that the formula for the eigenvalues can reproduce a known
rigorous expression on the Mathieu equation.