On commuting operators related to asymptotic symmetries in the atomic theory

There are many situations in physics where two types of symmetries coexist asymptotically withoutinterference. Let us bring up two examples of such a phenomena in the theory of atom. As it was shown in [1],there is a symmetry between the order of completion of the electronic levels of different atoms [2] and thespectra of the hydrogen atom [3,4]. Let us consider the multielectron problem of the electronic shells andsubshells structure as a function of atomic number. If one orders the electronic configuration in the coordinates(n , l), e.g. in the same coordinates in which were ordered the energy levels of the hydrogen atom (relations 1),the picture obtained does not reveal any structure or regularity (Figure 1). However, if the subshells are ordereddifferently (Figure 2), one gets clear-cut triangular structure. This ordering as a function of principal and orbitalquantum numbers, might be restructured in the form [1]:

Открыть: 1-BM-Commutation

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Fedor Alekseyevich Bogomolov (born 26 September 1946) (Фёдор Алексеевич Богомолов) is a Russian andAmerican mathematician, known for his research inalgebraic geometry and number theory. Bogomolov worked at Steklov Institute in Moscow before he became a professor at Courant Institute. He is most famous for his pioneering work on hyperkähler manifolds.