An alternative (and equivalent) way to describe what the translation operator determines is based on position-space wavefunctions. If a particle has a position-space wavefunction ψ ψ ( r ) , and T ^ ^ ( x ) acts on the particle, the new position-space wavefunction is ψ ψ ′ ( r ) = T ^ ^ ( x ) ψ ψ ( r ) defined by ψ ψ ′ ( r ) = ψ ψ ( r − − x ) .