Using Fourier transform in both temporal and spatial domain (that is, with integral kernel e j ω ω t + j k ⋅ ⋅ x ), its characteristic equation can be obtained: j ω ω c ~ ~ + v ⋅ ⋅ j k c ~ ~ = 0 → → ω ω = − − k ⋅ ⋅ v , which gives the general solution: c = f ( x − − v t ) , where f is any differentiable scalar function. This is the basis of temperature measurement for near Bose–Einstein condensate via time of flight method.