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In the bound states in the continuum (BIC) the binding energy is positive,and the mass of a composite particle is greater than the total mass of itsconstituents. In this work the BIC state is studied for the electron-protonsystem with using the ladder Bethe-Salpeter equation. We demonstrate that thereare two momentum space regions in which the electromagnetic interaction betweenthe particles is strongly enhanced, and the effective coupling constant isequal to $\alpha \sqrt{m_{p}/m_{e}}=0.313$, where $\alpha$ is the finestructure constant, $m_{p}$ and $m_{e}$ are the proton and the electron masses.This interaction resonance causes the confinement of the pair in the BIC statewith the positive binding energy of 1.531 of the electron mass. The integralequation for the bispinor wave function is derived. This normalized wavefunction which must be complex, was found numerically in the momentum andcoordinate spaces. It turned out that in the BIC state, the average radius forthe electron is equal to 48Fm, and the average radius for the proton is equalto 1.1Fm. This composite particle can exist exclusively in the free state, inwhich its properties, such as its form-factors, should only be studied. Inbound states with other particles, the composite loses its individuality.

The electron-proton bound state in the continuum with the positive binding energy of 1.531 of the electron mass