1. The problem statement, all variables and given/known data The translation operator T(a) is defined to be such that: T(a)ψ(x) = ψ(x+a) Show that: T(a) can be expressed in terms of the operator p = -iħ d/dx and T(a) is unitary. 2. Relevant equations T(a)ψ(x) = ψ(x+a) p = -iħ d/dx 3. The attempt at a solution I honestly have no idea how to start this expression, I figured there may be some way of doing it in a Taylor's expansion maybe, but I'm not sure how that would work, and that's the only guess I have on how to start this. Could anybody possibly give me some direction on where to start, please? Thank you very much.