8.2 Expectation value of
and
for the harmonic oscillator
As an example of all we have discussed let
us look at the harmonic oscillator. Suppose we measure the
average deviation from equilibrium for a harmonic oscillator in
its ground state. This corresponds to measuring
. Using
|
(8.17) |
we find that
|
(8.18) |
Qn Why is it 0? Sinilarly, using
and
|
(8.19) |
we find
More challenging are the expectation values
of
and
. Let me look at the first one first:
Now for
,
|
(8.22) |
Thus,
This is actually a form of the uncertainity
relation, and shows that