A toplogical view of a molecule along free electrons trajectories|
1. I sent Atiyah this paper and he replied with the paper, Complex Geometry of Nuclei and Atoms
2. Addendum: Making a drug without side effects(Sep. 18 2019)
We make the following claims which came up while working on the note, For quantum mechanical model on decision making
(1) A molecule such as enzymes, proteins has an oscillator activated by a unique 'resonance' frequency(or oscillators, see for superposition).
For, the amplitude x of an oscillator is governed by the equation
m(d2x)/(dt2) + c(dx)/(dt) + kx = F0cos(ωt+Δ), c=mγ, k = mω20
and the solution is given as x = ρF0cos(ωt+Δ+θ) and the relation between ρ2 and frequecy is as follows.
Adapted from Feynman Lectures on Physics, Vol I
Δω = γ when γ is small, which implies that a molecule is activated by a frequency 'very close' to the resonance frequency ω0(Refer to  and see also a induced precession) This explains why such molecules work with high-precision, just as a right tune can hear a specific station broadcast.
This claim could be proved like this. Mix two different-type enzymes, put it under an electric field and seperate into two group by varying frequencies of the electric field
(2) The 'resonance' frequency concept suggests a way of making a drug which manages to find a specific cell only, which means a drug without side effects. For example, a cancer cell would radiate a different wave from the one from a normal cell(Refer to ). So make a molecule activating by the wave of a cencer cell(i.e. a carrier to a cencer cell) and attach to a drug.Reference
(3) On how enzymes work, roughly speaking, wake up by a unique frequency => activate a motor moving towards a specific target => associate with the target and make change of free electrons distribution.
 Feynman Lectures on Physics, Vol I, 23-6
 Feynman Lectures on Physics, Vol I 28-4