International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. C, ch. 4.1, pp. 186187

Both electromagnetic waves and particles can be described by the wavefunction ψ(r), as a complex function of spatial coordinates, by the wavelength λ, the wavevector k, which indicates the direction of propagation and is of magnitude 2π/λ, the frequency ν or angular frequency in rad s^{−1}, and the phase velocity v (and the group velocity). Intensity in r is given by ψ(r)^{2}. These wavefunctions are solutions of the same type of differential equation [see, for example, Cowley (1975)]:
For electromagnetic waves, where k is the wavenumber, is the permittivity or dielectric constant and μ is the magnetic permeability of the medium; for most cases. The velocity of the waves in free space is otherwise , where is the refraction index.
For particles of mass m and charge q with kinetic energy E_{k} in fieldfree space, the wave equation (4.1.2.1) is the timeindependent Schrödinger equation and where (r) is the electrostatic potential function and the bracket gives the sum of the kinetic and potential energies of the particles.
Important nontrivial solutions of (4.1.2.1) are (after adding the time dependence) the plane wavefunctions or the spherical wavefunctions Thus, relatively simple semiclassical wave mechanics, rather than full quantum mechanics, is needed for interactions with no appreciable loss of energy. The interaction of the waves with matter depends on the spatial variation of the refractive index given by the spatial variations of the electron density or the electrostatic potential functions.
Electromagnetic waves can also be described in terms of energy quanta, photons, with energy given by Planck's law The values of E, ν, and λ of the electromagnetic waves used in general crystallography are scaled in Fig. 4.1.2.1 . It should be noted that there are several types of electromagnetic waves in the most important wavelength range near 1 Å, which are called Xrays (when generated in Xray tubes), γrays (when emitted by radioactive isotopes) or synchrotron radiation (emitted by electrons moving in a circular orbit).

Comparison of the energy, frequency, and wavelength of the electromagnetic waves used in crystallography (logarithmic scale). 
On the other hand, the beam of particles of mass m, moving with velocity v, behaves like waves with wavelength given by de Broglie's law or using for the kinetic energy of particles When relativistic effects are taken into account, where m_{0} is the rest mass and λ_{0} the nonrelativistic wavelength. Highenergy electrons ( Å) and neutrons ( Å) belong to the most prominent particles used in diffraction crystallography (see Table 4.1.3.1). However, lowenergy electrons ( eV, Å), protons or ions of elements with quite high atomic number and energy ( 10^{3}–10^{6} eV) are also used in scattering, channelling or shadowing experiments (see Section 4.1.5).

References
Cowley, J. M. (1975). Diffraction physics, Chap. 1. Amsterdam: NorthHolland.