We have seen that in certain experiments electrons produce patterns attributed to waves. From this observation, we concluded that electrons have wave-like properties. We also concluded that as the energy of electrons increases their wavelength decreases.

Electrons are a form of matter, so these waves are called matter waves. In this tutorial we will relate quantitative features of matter waves with familiar, measurable physical quantities such as energy, mass, and momentum. We will apply these relationships to forms of matter other than electrons, and see how these results can be applied to the electron microscope.