 A toplogical view of a molecule along free electrons trajectories

MyungHo Kim(mkim1795(at)gmail.com)

1. I sent M. 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 \begin{equation} m\frac{d^2x}{dt^2}+c\frac{dx}{dt}+kx=F_0 \cos(\omega t+\Delta), c=m\gamma, k=m{\omega_0}^2 \end{equation}

and the solution is given as $x=\rho F_0\cos(\omega t+\Delta+\theta)$ and the relation between ${\rho}^2$ and frequecy is as follows. Adapted from Feynman Lectures on Physics, Vol I

$\Delta \omega=\gamma$ when $\gamma$ is small, which implies that a molecule is activated by a frequency 'very close' to the resonance frequency $\omega_0$ (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.
(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.

Reference

 Feynman Lectures on Physics, Vol I, 23-6
 Feynman Lectures on Physics, Vol I 28-4