Electron excitation

Electron excitation is the transfer of a bound electron to a more energetic, but still bound state. This can be done by photoexcitation (PE), where the electron absorbs a photon and gains all its energy or by electrical excitation (EE), where the electron receives energy from another, energetic electron. Within a semiconductor crystal lattice, thermal excitation is a process where lattice vibrations provide enough energy to transfer electrons to a higher energy band such as a more energetic sublevel or energy level. When an excited electron falls back to a state of lower energy, it undergoes electron relaxation. This is accompanied by the emission of a photon (radiative relaxation/spontaneous emission) or by a transfer of energy to another particle. The energy released is equal to the difference in energy levels between the electron energy states.
In general, the excitation of electrons in atoms strongly varies from excitation in solids, due to the different nature of the electronic levels. The electronic excitation (or desexcitation) can take place by several processes such as: 
Electron excitation in solids.
Ground state preparation.
The energy and momentum of electrons in solids can be described by introducing Bloch waves into the Schrödinger equation with applying periodic boundary conditions. Solving this eigenvalue equation, one obtains sets of solutions that are describing bands of energies that are allowed to the electrons: the electronic band structure. The latter page contains a summary of the techniques that are nowadays available for modeling the properties of solid crystals at equilibrium, i.e., when they are not illuminated by light. 
Electron excitation by light: polariton.
The behavior of electrons excited by photons can be described by the quasi-particle named "polariton". A number of methods exist to describe these, both using classical and quantum electrodynamics. One of the methods is to use the concept of dressed particle. 