[yorwba]

But of course you can talk about simple physics without invoking quantum physics. What do you think physicists did before? Most everyday phenomena can be approximated very well by classical physics, and modeling the full wave-function for every particle wouldn't even get you any results in a reasonable time.

Since neurons are relatively large and dense, I expect a classical approximation wouldn't show any observable difference in behavior. Unless a deviation is shown, I don't think it is necessary to postulate things like Roger Penrose's quantum-gravity "explanation" of consciousness.