Is the wavefunction always an analytic signal?

[olgerm]

Is wavefunction always analytic signal?
Is imagnigray part of wavefunction hilbert transform of real part of wavefunction?

 

[A. Neumaier]

Is the wavefunction always an analytic signal?
Is the imaginay part of the wavefunction a hilbert transform of the real part of the wavefunction?

No. It can be any square integrable function.