Find (p,t) for the free particle in terms of the function (k) introduced in Equation

Find ϕ (p,t) for the free particle in terms of the function ϕ (k) introduced in Equation 2.101. Show that for the free particle |ϕ (p,t)|² is independent of time. The time independence of |ϕ (p,t)|² for the free particle is a manifestation of momentum conservation in this system.

Equation 2.101

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(x, 1) = 1 √2π9 (1) dk. (k) ei (x-1) (2.101)