Original hypothesis
Let’s go back to our hypothesis [9]. Every electron in atom A has some definite value of potential for any configuration of electrons. The value of potential for electron with number i can be expressed by the following formula:
\(u_{i}=\frac{N}{r_{A,i}}-\sum_{k\neq i}\frac{1}{r_{\text{ik}}}\)(1)
In formula (1) N is the number of electrons in atom А, i.e. the charge of the nucleus, \(r_{A,i}\) is the distance between electron with index i and the nucleus, \(\ r_{\text{ik}}\) is the distance from this electron to the electron with index k . The summation is being carried for all k from 1 to N except i .
Let’s consider function Φ=\(u_{1}-u_{2}\), i.e. the potential difference of electrons “1” and “2” that have the same spins as was pointed before. This function is defined for any point of the interchange trajectory of electrons “1” and “2” and has the same quality as the wave function Ψ itself, i.e. at the ends of the interchange trajectory it has opposite signs according to formula (1). It means that inside the interchange trajectory at least one point where function Φ turns to zero exists. The meaning of our hypothesis [9] is as follows: for the points with Φ=0 Ψ=0 too, i.e. nodal points of these functions on the interchange trajectory are the same. This means that the set of Φ nodal surfaces is a subset of the Ψ nodal surfaces set. Function Ψ turns to zero not only for the configurations with Φ=0, i.e. \(u_{1}\)=\(u_{2}\), but for all the cases \(u_{i}\)=\(u_{j}\) if spins of electrons “i” and “j” are the same. Let’s consider the interchange trajectory of electrons “1” and “2” with arbitrary coordinates in case when the coordinates of other electrons and nuclei are fixed. Let’s the initial distance between the electrons “1” and “2” is decreasing and approaching to zero. Then distances between the zero points of Ψ and Φ turn to zero too (even if the distances were not the same initially), i.e. these points coincide in the limit. This, of course, is not a proof of our hypothesis but a suggestion giving some hope that it is valid.