# Operators, Eigenfunctions, and Symmetry

### From FSUPhysicsWiki

In this chapter, we introduce the concept of operators and linear vector spaces, both of which are of central importance to the mathematical formalism of modern quantum mechanics. As stated earlier, all observable properties of a system are now described by operators that act on the wave function of the system. The wave function itself is described as an abstract state vector belonging to a linear vector space. We will show how to formulate the Schrödinger equation in terms of such quantities, as well as obtain a number of other important results, such as a formal proof of the Heisenberg Uncertainty Principle.

We also give a brief introduction to the role that symmetry plays in quantum mechanics, and how it can be an aid in solving problems in quantum mechanics.