Chem120A Notes 9/10/08
Different versions of the postulates of quantum mechanics
Postulate III:
“Suppose that
A
ˆ
is an operator corresponding to an observable and that there is a set of
identical systems in state
s
Ψ
.
Suppose further that
s
Ψ
is an eigenfunction of
A
ˆ
.
s
a
s
a
A
Ψ
=
Ψ
ˆ
where
a
s
is a number.
Then, if an experimentalist makes a series of measurements of a quality
corresponding to
A
ˆ
on different members of the set the result will always be
a
s
.
It is only when
s
Ψ
and
A
ˆ
satisfy this condition that an experiment will give the same result on each
measurement.
Postulate IV:
“Given an operator and a set of identical systems characterized by a function
s
Ψ
that is
not
an eigenfunction of
A
ˆ
, a series of measurements of the property corresponding to
A
ˆ
on
different members of the set will not give the same result.
Rather, a distribution of
discrete
results will be obtained, the average of which will be:”
τ
d
d
A
A
Ψ
Ψ
Ψ
Ψ
=
∫
∫
*
*
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 Spring '07
 Whaley
 Physical chemistry, pH, dependant schrodinger equation, Time Dependant Schrödinger

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