Modification of analytical expression of electron dynamical diffraction

Assuming that the wave function phi=e(eta), the Schrodinger equation can be written as Delta(xy)eta+4piik(xy)del(xy)eta+4piik(z)partial derivativeeta/partial derivativez+ V(r)+partial derivative(2)eta/partial derivativez(2)+(deleta)(2) =0. Neglecting the last two terms, an analytical expression of electron dynamical diffraction was derived by Qibin YANG et al. In this paper, the analytical expression is modified by further considering the second-order differential term partial derivative(2)eta/partial derivativez(2). When the accelerating voltage is not very high, or the sample is not very thin, the reciprocal vector g is large, the modification of the second-order differential is necessary; otherwise it can be neglected.