The Momentum Operator

We determine the momentum operator by requiring that, when we operate with on , we get times the same wave function.

This means that for these definite momentum states, multiplying by is the same as multiplying by the variable . We find that this is true for the following momentum operator.
We can verify that this works by explicit calculation.

If we take our momentum operator and act on a arbitrary state,

it gives us the right for each term in the integral. This will allow us to compute expectation values for any variable we can represent by an operator.

Jim Branson 2013-04-22