1. The problem statement, all variables and given/known data A translation operator T(a) coverts ψ(x) to ψ(x+a), T(a)ψ(x) = ψ(x+a) In terms of the (quantum mechanical) linear momentum operator p_x = -id/dx, show that T(a) = exp(iap_x), that is, p_x is the generator of translations. Hint. Expand ψ(x+a) as a Taylor series. 2. Relevant equations Groups? 3. The attempt at a solution I'm lost at the hint. To expand ψ(x+a) as a Taylor series, don't I need a point around which to expand it?