  Relations between particle and wave properties for charge carriers in
periodic potentials of crystalline metals and semiconductors are derived. The
particle aspects of electrons and holes in periodic potentials are considered
using properties of quasimomentum (QM), while the wave aspects are described
employing wave packets of Bloch waves. The two aspects are combined in the
derivation of QM-wavelength relations for energy bands of arbitrary
nonparabolicity and nonsphericity. An effective mass relating electron QM to
its average velocity for spherical energy bands is defined and used to
calculate energy dependences of wavelengths for electrons in narrow gap
semiconductors, graphene and surface states of topological insulators. An
uncertainty relation between electron quasimomentum and its spatial coordinate
in periodic potentials is derived. It is emphasized that the described
properties apply to the average (not instantaneous) electron behavior.
Analogies between the wave and uncertainty properties of electrons in
crystalline solids and those in vacuum are traced.
