An exercise. A property of the Fourier transform of wavelet

Question

In the book "An Introduction To Wavelet Analysis" by David F. Walnut, there is,
Exercise 7.45. Show that if $\psi(x)$ is a wavelet, then $\sum\limits_{j}{\left|\hat{\psi}(2^j\gamma)\right|^2} = 1$
Here, $\psi(x)$ is the mother wavelet function, and $\hat{\psi}(\gamma)$ is the Fourier transform of $\psi(x)$. $\hat{\psi}(\gamma) = \int_{-\infty}^{\infty}\psi(x)e^{-2{\pi}i{\gamma}x}dx$
I can not prove it.
But testing with Haar Wavelet by Matlab, it seems right.
Can someone tell me if it's right, and How to prove it?
And thank you for your time!