Engineering Physics Annotation << Back TWO SOLUTIONS OF THE KLEIN-GORDON EQUATION FOR HYDROGEN-LIKE ATOMS AND MICROHYDROGEN A.I. LAPTUKHOV, N.V. SAMSONENKO, V.A. LAPTUKHOV, M.V. SEMIN A simple derivation of two solutions of the Klein-Gordon equation for a system of the nucleus of an atom and an electron in the approximation of point particles is given. It is shown that taking into account the finite size of the proton for the first solution (for the hydrogen atom) practically did not change the binding energy of particles, while for the second solution the binding energy greatly decreased: from 507 keV to 5–20 keV. Thus, this solution describes a previously unknown electrically neutral particle (microhydrogen, but not a neutron), whose size is almost the same as the size of a free electron Re=ħ/(mec)=3,86∙10–13 m. It is important that the formation of such particles makes it possible to explain the release of large amounts of excess energy in low-energy processes, which are currently being actively studied by many groups of scientists in Japan, Italy, the USA, China, Russia and other countries of the world. Keywords: Klein-Gordon equation, non-point particles, binding energy, microhydrogen, low-energy processes. DOI: 10.25791/infizik.8.2022.1279 Pp. 12-20.