We have now defined p ^ ^ in terms of translation operators. It is also possible to write a translation operator as a function of p ^ ^ . The method consists in expressing a given translation as a huge number N of consecutive tiny translations, and then use the fact that infinitesimal translations can be written in terms of p ^ ^ : T ^ ^ ( x ) = lim N → → ∞ ∞ ( T ^ ^ ( x / N ) ) N = lim N → → ∞ ∞ [ 1 − − i x ⋅ ⋅ p ^ ^ N ℏ ℏ ] N which gives the final expression: