Ambartsumian’s scientific contribution is not limited to studies on various problems of modern astronomy and astrophysics.
In a number of his studies, important questions concerning the theoretical physics and mathematics are solved. Part of them appeared in connection with researches of astrophysical nature. For example, the harmonious theory of light scattering, based on the new, very fruitful principle of invariance, was created for studying of atmospheres of planets and stars. Another such example is the two-dimensional generalization of Poisson’s law of distribution of random numbers for a case when the corresponding numbers are not completely independent from each other. This generalization was obtained by working out the theory of fluctuations for statistical study of the absorbing clouds making the interstellar medium.
However, some of Ambartsumian’s works on physics and mathematics, mainly of the Leningrad period of his activity, are not directly connected with astrophysical problems and represent an independent scientific interest.
Among them, first of all it is necessary to note the research on the theory of Eigen values of the differential equations. In this study the problem contrary to the widely known in the mathematical physics problem of Storm-Liuville was for the first time formulated and preliminarily worked out. The questions, which were put forward in this research, didn’t find at that time any responses in the scientific world. The reason for this silence, apparently, was the fact that the author of this on essence mathematical research was an astrophysicist, and the paper containing his results was published in the German physical journal “Zeitschrift fur Physik” (“Journal on Physics”). However, in decades the scientists paid to it necessary attention, and serious studying of these questions by mathematicians began, which was marked by the birth of a new direction in the mathematical physics.
A great scientific interest represents also the study (together with D.D. Ivanenko), in which for the first time it was shown that the atomic nucleus beside protons should contain also neutral particles. This new idea contradicted the understanding dominating at that time in the nuclear physics according to which in an atomic nucleus beside protons there also exist electrons. It is remarkable that the conclusion about the presence of neutral particles in an atomic nucleus was made before the discovery of neutrons. As it is known, further studies in this area, in particular the discovery of neutrons, confirmed this conclusion, and the new understanding about the structure of the atomic nucleus obtained a final recognition.
In another study (also together with D.D. Ivanenko), a conclusion was justified about the imperfection of existing at that time quantum-mechanical understandings about a point structure of electrons and on this basis a question about the necessity of working out of a new theory on the structure of electrons was put forward.
In conclusion of this section we will notice that Ambartsumian’s some researches of this period are devoted to the unified field theory, linear geometry of functional space, etc.