The function ?(x) displayed in Eq. 38-19 describes a free particle, for which we assumed that U(x)

Question:

The function ?(x) displayed in Eq. 38-19 describes a free particle, for which we assumed that U(x) = 0 in Schrodinger's equation (Eq. 38-15). Assume now that U(x) = U0 = a constant in that equation. Show that Eq. 38-19 is still a solution of Schr6dinger's equation, with now giving the angular wave number k of the particle.