Where did the operator come from?
For momentum, why is it different from just p ?
The operator is a function which, when acting on
in the probability integral, produces an expectation value for
that quantity In the Schrödinger representation.
The operator for x is just x , for
it is just
.
But for momentum we have to find a way to write p
in terms of x or t , so that we can do the integral
The trick we found was to note that
This then says that we can do the integral by equating
,
the momentum operator in the Schrödinger representation.