Ψ Ψ ( k , t ) = ( 2 π π a ) 3 / 2 e − − a k ⋅ ⋅ k / 2 e − − i E t / ℏ ℏ = ( 2 π π a ) 3 / 2 e − − a k ⋅ ⋅ k / 2 − − i ( ℏ ℏ 2 k ⋅ ⋅ k / 2 m ) t / ℏ ℏ = ( 2 π π a ) 3 / 2 e − − ( a + i ℏ ℏ t / m ) k ⋅ ⋅ k / 2 .