No it doesn't. I understand the math and quantum physics just fine. There are a few instances of formerly very brilliant people going a little unhinged (e.g. Penrose) and a lot of instances of people babbling about things they only display a superficial understanding of (e.g. Hameroff) and some people with a superficial understanding of physics getting confused about the distinction between first- and third-person perspectives and between epistemology and ontology (e.g. the panpsychics).

And then there's everyone else who creates increasingly accurate models that do a better job of describing and predicting our observations and don't get confused by language-games around the word "exist".

(Feel free to share any math and/or physics you think is relevant. I understand it. It's not gobbledygook to me. For instance, I know what a Hamiltonian is, and how it's used both in QM and classical mechanics. Might take me a bit of a refresher to solve any nontrivial problems, though--it's been a while.)

With the type of reasoning you're using here, we may as well retain vitalism. There's really no experiment that disproves it--yes, there's no difference in molecules, and yes, life seems to work according to the same mechanism as everything else, and no, there's no evidence of anything else impinging on the process, and yes, we can take out subcomponents and replace them and it still works...BUT maybe there is still a vital spark that distinguishes life from non-life, and there's no experiment that can disprove it.

This is exactly the sort of thing that Occam's razor is there to cut away. It's exactly why Popper requires falsifiability. You get arbitrarily many experimentally irrelevant ideas tagging along with your scientific theories otherwise...and have the associated danger that you start thinking the irrelevant ideas are relevant.