Symmetries are a key idea in physics. In the classical world, they are associated to conservation laws, courtesy of Emmy Noether. The same, and more, is true in the quantum world. In this chapter we explore how symmetries manifest themselves in quantum mechanics. Special attention will be given to time evolution and the role of SU(2) and angular momentum

Bulk semiconductors. Stimulated transitions: selection rules. Joint density of states. Absorption coefficient and gain in bulk semiconductors; Bernard-Duraffourg condition; transparency condition and differential gain. Spontaneous emission; bimolecular recombination: low and strong injection. Nonradiative recombination. Shockley-Read-Hall model. Auger recombination. Surface recombination. Radiative efficiency.

We learn time-dependent perturbation theory, where we focus on finding the probability that an applied perturbation causes a transition between energy levels of the unperturbed Hamiltonian. We calculate the probability amplitude for a transition from an initial state to a final state subject to a time-dependent perturbation. We learn that an excited state in an atom has a finite lifetime due to spontaneous emission. We learn that electric dipole transitions obey selection rules.