Operators allow us to compute the expectation value of some physics quantity given the wavefunction.
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 . The expectation value of in the state is
* Example:
A particle is in the state
.
What is the expectation value of ?*
For any physical quantity
, the expectation value of
in an arbitrary state
is
Gasiorowicz Chapter 3
Griffiths Chapter 1
Cohen-Tannoudji et al. Chapter
Jim Branson 2013-04-22