QUANTUM CONDITIONS IN MEMBRANE-TRANSPORT CONTROLLING NERVOUS EXCITATION

While the electric field in synthetic ion-exchange membranes has been found to be described by the equations of Teorell, and Meyer and Sievers, in the case of isotonic osmosis, Planck-Goldman's potential, first found in the nerve, is important. In contrast to Teorell's equation the latter integral represents a potential function. Beneath this integral with respect to position we have to explore the integral with respect to time as results from nervous excitation. This assumes a minimum value if a potential controls its course. Indeed, this integral, the action, yields Planck's constant. To explain this phenomenon, membranes must be considered as polymers doped with Na and/or K atoms. While this process results in the capture of the valence electrons of the dopants by any traps of the membrane, the interaction of these electrons with the remaining cations continues. In this way, the membrane merely represents the carrier of an atomic process resulting in the diffusion of the cations from trap to trap. According to potential theory we have to regard the K bullet Na bullet potentials in nervous excitation as stationary while the transition from the first state into the second state will be controlled by the Green function. Applying to the partial differential equation of the action controlling Green's function, Jacobi's method of the complete integral we come to the goal if the minimum value of the variational problem in space and time is determined by using Dirichlett's integral. From this we find that in a doped polymer the friction controlling the ion transport depends only on the electrons of the dopant atoms. Finally, from the experimentally determined values of the frictional coefficients one obtains a value of the action which is agreement with Planck's constant to within 6%. As our calculation is based only on classical methods and no quantum conditions were taken into account this result is surprising.