Since A (t) has a classical Fourier series with only the lowest frequency, and the matrix element A mn is the (m − n) th Fourier coefficient of the classical orbit, the matrix for A is nonzero only on the line just above the diagonal, where it is equal to √ 2 E n. The matrix for A is likewise only nonzero on the line below the diagonal, with the same elements. Thus, from A and A, reconstruction yields 2 X ( 0 ) = ℏ ℏ [ 0 1 0 0 0 ⋯ ⋯ 1 0 2 0 0 ⋯ ⋯ 0 2 0 3 0 ⋯ ⋯ 0 0 3 0 4 ⋯ ⋯ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱ ⋱ ] , and 2 P ( 0 ) = ℏ ℏ [ 0 − − i 1 0 0 0 ⋯ ⋯ i 1 0 − − i 2 0 0 ⋯ ⋯ 0 i 2 0 − − i 3 0 ⋯ ⋯ 0 0 i 3 0 − − i 4 ⋯ ⋯ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱ ⋱ ] , which, up to the choice of units, are the Heisenberg matrices for the harmonic oscillator. Both matrices are hermitian, since they are constructed from the Fourier coefficients of real quantities.