Assume a particle initially has a momentum space wave function described by a normal distribution around some constant momentum p 0 according to φ φ ( p ) = ( x 0 ℏ ℏ π π ) 1 / 2 exp ⁡ ⁡ ( − − x 0 2 ( p − − p 0 ) 2 2 ℏ ℏ 2 ) , where we have introduced a reference scale x 0 = ℏ ℏ / m ω ω 0 , with ω ω 0 > 0 describing the width of the distribution—cf. nondimensionalization. If the state is allowed to evolve in free space, then the time-dependent momentum and position space wave functions are Φ Φ ( p , t ) = ( x 0 ℏ ℏ π π ) 1 / 2 exp ⁡ ⁡ ( − − x 0 2 ( p − − p 0 ) 2 2 ℏ ℏ 2 − − i p 2 t 2 m ℏ ℏ ) , Ψ Ψ ( x , t ) = ( 1 x 0 π π ) 1 / 2 e − − x 0 2 p 0 2 / 2 ℏ ℏ 2 1 + i ω ω 0 t exp ⁡ ⁡ ( − − ( x − − i x 0 2 p 0 / ℏ ℏ ) 2 2 x 0 2 ( 1 + i ω ω 0 t ) ) .