##

Expectation Values

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

We can move the
between just before
anticipating the use of linear operators.

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

The Dirac
Bra-ket notation
shown above is a convenient way to represent the expectation value of a variable given some state.
* 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

**The expectation values of physical quantities should be real**.
**Gasiorowicz Chapter 3**

**Griffiths Chapter 1**

**Cohen-Tannoudji et al. Chapter **

Jim Branson
2013-04-22