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**Problem**

A free particle of mass [tex]m[/tex] moving in one dimension is known to be in the initial state

[tex]\psi(x, 0) = \sin(k_0 x)[/tex]

a) What is [tex]\psi(x, t)[/tex]?

b) What value of [tex]p[/tex] will measurement yield at the time [tex]t[/tex], and with what probabilities will these values occur?

c) Suppose that [tex]p[/tex] is measured at [tex]t=3 s[/tex] and the value [tex]\hbar k_0[/tex] is found. What is [tex]\psi(x, t)[/tex] at [tex]t > 3 s[/tex]?

**Attempt at Solutions**

Well one question I have is this: how is this a valid state function for a free particle if it is non-square integrable? Generally, for any free particle, doesn't the wavefunction have to be square-integrable?