A complex Morlet wavelet looks like this:
$$\psi(t) = C \cdot e^{i \omega t} \cdot e^{-t^2/2}$$
Here $\omega$ is the frequency and $C$ is some normalization constant. The first exponential represents the oscillation, and the second exponent is the Gaussian-like envelope. However, what should $C$ be?
First, why is $C$ even necessary? Admissibility of a wavelet is based on finite support (which the Morlet wavelet has practically, if not really) and its integral over its whole range summing to $0$, which is does regardless of $C$'s value.
Torrence and Compo's A Practical Guide to Wavelet Analysis, on whose work mlpy's wavelets are based, argue for the constant $\pi^{-\frac{1}{4}}$ to "ensure a total energy of unity". Wikipedia's Morlet wavelet page gives the more complicated coefficient $\pi^{-\frac{1}{4}} \left(1 + e^{-\sigma^2} - 2e^{-\frac{3}{4}\sigma^2}\right)^{-\frac{1}{2}}$, where $\sigma$ is a parameter allowing some kind of tradeoff between time and frequency resolution. I'm having a hard time rectifying these two different approaches.
Finally, does $C$'s value have any relation to whether you want the resulting frequencies to be on a logarithmic scale, or a linear scale?