Massachusetts Institute of Technology
Department of Physics
Physics 8.04 Wed Oct 11 21:39:07 EDT 1995
Quantum kinematics may be carried out entirely with nothing more than the framework laid out in the preceding lecture notes on ``Quantum States, Observables and Probability Distributions.'' In principle, with just the physics in those notes, the student may solve all the problems which will be presented in the rest of this course. However, as complete as the framework we now have is, it is still inconvenient at times in its application as it lacks significant mathematical infrastructure.
Operator theory will provide us with the missing structure. One of the most important uses of operators in quantum theory is in the calculation of averages. We shall thus use this as the context in which to introduce operators into our theory and, in fact, use the calculation of averages as the defining point for our quantum mechanical operators. As no physics will be introduced in this note beyond that of the preceding set of notes, you may think of everything in this note as definitions and derivations based on this physics already presented in previous course material.