##

Dirac Bra-ket Notation

A state with definite momentum
.

A state with definite position
.

The **``dot product''** between two abstract states
and
.

This dot product projects the state
onto
and represents the amplitude to go from
to
.
To find the probability amplitude for our particle to by at any position
,
we dot the state of definite
into our state
.

To find the probability amplitude for our particle to have a momentum
,
we dot the state of definite
into our state
.

Jim Branson
2013-04-22