The space translation operator T ^ ^ ( Δ Δ r ) acts on a wavefunction to shift the space coordinates by an infinitesimal displacement Δ r. The explicit expression T ^ ^ can be quickly determined by a Taylor expansion of ψ (r + Δ r, t) about r, then (keeping the first order term and neglecting second and higher order terms), replace the space derivatives by the momentum operator p ^ ^ . Similarly for the time translation operator acting on the time parameter, the Taylor expansion of ψ (r, t + Δ t) is about t, and the time derivative replaced by the energy operator E ^ ^ .