How do we go from the operator exponential involving p-hat^2 to the exponential involving the eigenvalue p^2? Is this by taking the definition of the operator exponential as it's power series expansion of operators, then acting term by term on |p>?
There are two ways to do it: (1) use Taylors' expansion of the exponential and apply the operator powers to the momentum eigenket or (2) (easier) remember the theorem that if \hat{A}|a>=a|a> then for any function we have f(\hat{A})|a>=f(a)|a>
