# Wave function - expected momentum is infinite

I have a wave function, say \begin{align} \Psi(x) = xe^{ikx} \end{align}

And I want to find the expectation value for momentum, $$

$$

It's not working out to an integral I can evaluate though \begin{align}

&= \int \limits_{-\infty}^\infty dx \Psi^*(x)(-ih\frac{d}{dx})\Psi(x) \\ & = hk \int \limits_{-\infty}^\infty dx~xe^{-ikx} e^{ikx} (1 + x) \\ & = hk \int \limits_{-\infty}^\infty dx(x^2 + x)=\infty. \end{align}

Does this have a special meaning? Or am I doing something terribly wrong

• @JOE How about free particle eigenstate $e^{ikx}$ with momentum eigenvalue $\hbar k$. But it is not normalizable – K_inverse Nov 1 '18 at 8:32
• @K_inverse I think $e^{ikx}$ is normalized – Alter Nov 1 '18 at 8:44