The semiclassical time derivative of a matrix element is obtained up to a factor of i by multiplying by the distance from the diagonal, i k A m ( m + k ) ≈ ≈ ( T 2 π π d A d t ) m ( m + k ) = ( d A d θ θ ) m ( m + k ) . since the coefficient A m (m + k) is semiclassically the k th Fourier coefficient of the m th classical orbit.