Being a true disciple of Niels Bohr, Wheeler first of all learned the idea of quantizing the atomic energy levels of his great teacher. So he asked himself a question. It is well known that an electron and a proton form a hydrogen atom, two hydrogen atoms form a hydrogen molecule, and if we do not have hydrogen, and so-called Positronium, that is, a system consisting of an electron and a positron, an electron antiparticle predicted by Paul Dirac (and underlying concepts of "holes" in solids)- would be stable such a system? By the way, such an atom can have two states depending on the orientation of the spin: parapositronium (spins are antiparallel-then this system is more stable) and orthopositronium (the spins are parallel; then this system is less stable, its binding energy is higher and, therefore, some time after the radiation photon, it can go to parapositronium, that is, a spin flip occurs) [1, 2]. Soviet scientists [5, 6] were interested in this problem since 1949, but obviously they do not cite J.A. Wheeler as the author of the idea, preferring E. Hylleras and A. Ore [3, 4] which are late by 1 year at least. How will elementary objects that are different in their physical essence bind to "atoms"? Physicists are interested not only in the binding of an electron and a proton to a hydrogen atom, but, also in the binding of an electron and a hole to an exciton, and then, just as two hydrogen atoms create a hydrogen molecule, the binding of two excitons to a biexciton or, in a more chemical language, an exciton molecule. Who would have thought that in 1946 Wheeler could foresee the existence of exciton molecules in semiconductors? This area of science is developed after 1946, a lot of scientific schools throughout the world in connection with the most direct technological interest. Both in Russia, in the former Soviet republics and in the West, the problem of excitons and biexcitons (for example, biexcitons were predicted independently by Moldovan physicist Svyatoslav Moskalenko in 1958 [7] and by American Murray Lampert from Princeton University in the same year [8] ), boson condensate were of wide interest (see, for detail [9]).