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## Lecture (xx minutes)

Slides: qmoperators_wiki.ppt

In the case of continuous observables where continuous wave functions represent the quantum state, operators take the form of differential operators (momentum, energy) or the variable itself (position). At this stage, it is too early to discuss the differences between the position and momentum representations; we implicitly use the position representation. Relate to matrices of the Spins course.

This lecture is really the introduction to the activity in which students operate on different wave functions with different operators to illustrate that various functions may or may not be eigenfunctions of the operator. They identify the eigenvalues if the functions are eigenfunctions.

After the activity, the physical significance of the operators is discussed.

$$\hat{p} = - i\hbar \frac{d}{dx}$$

$$\hat{H}= \frac{1}{2m}\hat{p} \hat{p} = \frac{ - \hbar ^2}{2m} \frac{d^2}{dx^2}$$