While looking up spherical harmonics (on the validity of analysing them in real-space in a transition metal crystal structure), I came across this: http://shpenkov.janmax.com/hybridizationshpenkov.pdf (published in the hardonics journal...? I haven't really come across the journal before so I'm not too sure as of the validity of its peer-review process). The author argues mainly that because "hybridization as a mathematical mixing of qualitatively opposite properties (real and complex numbers) is physically impossible and hence unreal", QM incorrectly describes the atomic structure.
"...The mixing of these complex functions, contained “real” and “imaginary” quantities, together, as it has been done in quantum mechanics, is inadmissible, just like it is impossible, e.g., to mix together the electric and magnetic fields and then to ascribe to the obtained mixture the properties inherent only in the electric field (or, vice versa, only in magnetic). Thus, hybridization as a mathematical mixing of qualitatively opposite properties is physically impossible and hence unreal. It is merely a mathematical trick used by creators of QM at the earliest stage of its building..."
It is interesting because I've always accepted the Born rule without questioning how it has been derived (As so far I've been using QM mainly as a predictive tool for alloy properties in the context of alloying additions to a composition, rather than working on the theory behind it). A quick look-up of the Born rule shows that the square of the wavefunction arises from the assumption that a measurement of an observable will produce an eigenvalue as a result, and the exact perspective depends on the QM interpretation (Which I know very little about) see here. Ignoring the hadronics journal article itself (which has managed to get me curious, and thinking), my question is then (out of curiosity) two-fold:
- If there is any physical meaning to the imaginary terms. And if there is - is something being missed out when one combines the terms to obtain the real orbitals?
- Following from that, how valid would an argument that the linear combination of real and complex numbers are "physically impossible and hence unreal" be? I suspect that the answer to this is in the links to the older questions (since the are complex conjugates), and I will be going through them.
Edit notes 1: In the process of updating the question and reading up on the topic to update the question, I have found that similar questions have been asked before: see here and here... Following that, I have updated the question.
Edit notes 2: Probably answering my own question, but a related answer to question 1 is found here.