Étude on the one-dimensional periodic potential

All the formulas pertinent to dynamic diffraction in either the Bragg geometry or the Laue geometry are derived for an arbitrary one-dimensional periodic potential for which the reflection amplitude $(r)$ and the transmission amplitude $(t)$ for a single period are known. These formulas are derived by strictly algebraic methods. The diffraction of neutrons by monatomic and diatomic ideal single crystals is analyzed as an example. A general relation between the phases of the reflection and transmission amplitudes is proved by a gedanken experiment for an arbitrary nonabsorbing potential barrier.