The calculation of electron diffraction intensities by the multislice method

The calculation of wave functions of scattered electrons by the multislice method of Cowley and Moodie with a finite number of beams is shown to lead to the solution of a finite, closed set of differential equations in the limit that the slice thickness approaches zero. The solution is normalized but differs from the exact wave function unless sufficient beams are included in the calculation. Hence, normalization is not sufficient to ensure that the computed wave function equals the exact wave function. The implications of this result for numerical work are discussed.