You can also see this site http://gpcpublishing.com/index.php?journal=gjp&page=article&op=view&path[]=367&path[]=pdf_17 . See the equations (1) and (2) on page 2. It can be observed that wave-functions for electron and positron are quite different.
The conclusion from the linked paper... ....... 1. The frequency of the waves that comprise the three dimensional wave structure of the particle is based on the particle's mass (via the calculation shown above). 2. A particle's charge is defined by either an outward or inward flowing phase wave. A neutral particle would have no net phase flow inward or outward, but may contain regions of either inward or outward flow, which cancel out in the region surrounding the particle. 3. The completed wave function must satisfy both the Classical and Schrödinger wave equations. ........ Let's consider a hypothetical particle (not anti particle) with mass equal to electron and positive +e charge, will this particle have different wave function than positron? No, it will not, clearly establishing that there is no concept of anti_wave.
On the contrary, they differ only in the sign of the last term in brackets, so they are very closely related, just as the expressions in the link I provided were. (I am not sure however about the source you are using, by the way. It seems to be a pay-to-publish journal of no great repute.) But anyway, this is what one would intuitively expect: expressions that are in some sense mirror images of each other with sign changes. The term "antiwave" , which The God understandably takes exception to, is certainly not a very clear one in this context. It does not have a recognised meaning in physics, so far as I am aware. It might naively be taken to be a wave out of phase with the equivalent "wave", for instance. Clearly that is not the case here, as nothing correlates the phases of wave-particles that have not interacted. But I am not going to claim any great expertise on this: as I say, it was out of scope for us chemists.
You are referring to wave function equation, the true physical significance of wave function is to get the probability of presence if particle.