Eigenvalues of energy in j (l + 1/2, l ‐ 1/2) electron state in the hydrogen atom derived from the relativistically modified Schrödinger equation

Abstract

In the hydrogen atom, the eigenvalues of energy in j (l + 1/2, l ‐ 1/2) electron state cannot be correctly evaluated from the nonrelativistic Schrödinger equation. In order to express the relativistic properties of the wave equation for a particle with 1/2 spin, the Schrödinger equation is relativistically modified. The modified Schrödinger equation is solved for consistency with the eigenvalues of electron's energy derived from the Dirac equation. Based on the consistency of their eigenvalues, the different electron state is expressed. The microwave emission (e.g., 21 cm radio wave) by the hydrogen atom was thus predicted from this state.