The change of the definition of $\alpha$ from #14 and #15 has to be reverted again to have a more consistent definition of the Hermite functions for the Fourier transforms.
With the current definition, the real/complex behaviour of the Hermite functions is quite confusing for both the time/space and the frequency domain 😵💫
If the definition of $\alpha$ is changed, this could be resolved and the Hermite functions would all be real in the space/time domain.
The change of the definition of $\alpha$ from #14 and #15 has to be reverted again to have a more consistent definition of the Hermite functions for the Fourier transforms. With the current definition, the real/complex behaviour of the Hermite functions is quite confusing for both the time/space and the frequency domain 😵💫 If the definition of $\alpha$ is changed, this could be resolved and the Hermite functions would all be real in the space/time domain.