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PHY4604
R. D. Field
Department of Physics
Chapter3_7.doc
University of Florida
Example: Position and Momentum (2)
Transformation from xrep to p
x
rep:
To transform from the x
representation (
i.e.
positionspace) to the p
x
representation (
i.e.
momentum
space) we insert a complete set of
x>
states as follows:
∫
∫
>
<
=
>
><
<
>=
>=<
=<
dx
x
x
p
dx
x
x
p
I
p
p
p
x
x
x
x
x
)
(






)
(
ψ
where
<p
x
x>
is the “transformation function”. To go the other way around
we insert a complete set of
p
x
>
states as follows:
∫
∫
>
<
=
>
><
<
>=
>=<
=<
x
x
x
x
x
x
dp
p
p
x
dp
p
p
x
I
x
x
x
)
(






)
(
where
<xp
x
> = (<p
x
x>)*
is the “transformation function”.
The Transformation Function <xp
x
>:
This transformation function is
arrived at by solving
(p
x
)
op
p
x
> = p
x
p
x
>
or
(p
x
)
op
<
xp
x
> = p
x
<
xp
x
>
→
>
<
=
>
<
−
x
x
x
p
x
p
dx
p
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This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.
 Spring '07
 FIELDS
 mechanics, Momentum

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