Abstract
The Crank-Nicolson finite difference method is introduced as a real-space method for the calculation of electron scattering in transmission electron microscopy. The difference equation is based directly on the high-energy approximation of the Schrödinger equation. Contrary to previously published direct-space methods, proof is presented for the unconditional stability of the Crank-Nicolson method both for periodic as well as non-periodic boundary conditions. Comparisons between Crank-Nicolson and Bloch wave calculations show excellent agreement.
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