We can use operators to help us compute the
expectation value
of a physical variable.
If a particle is in the state
,
the normal way to compute the expectation value of
is

If the variable we wish to compute the expectation value of (like ) is not a simple function of , let its operator act on

We have a shorthand notation for the expectation value of a variable in the state which is quite useful.

We extend the notation from just expectation values to

and

We use this shorthand

Jim Branson 2013-04-22