Here is an example showing that these two descriptions are equivalent. The state | a ⟩ ⟩ corresponds to the wavefunction ψ ψ ( r ) = δ δ ( r − − a ) (where δ δ is the Dirac delta function), while the state T ^ ^ ( x ) | a ⟩ ⟩ = | a + x ⟩ ⟩ corresponds to the wavefunction ψ ψ ′ ( r ) = δ δ ( r − − ( a + x ) ) . These indeed satisfy ψ ψ ′ ( r ) = ψ ψ ( r − − x ) .