“Spinless” Hydrogen: Energy Eigenvalues

Brian P. Anderson

T. Roy

Thomas J. Greytak, Daniel Kleppner, Richard W. Cline +1 more

Akaninyene Daniel Antia, Eno E. Ituen, U.S. Jim +1 more

We have obtained the approximate solutions of the Klein–Gordon equation with the Yukawa ring-shaped potential, by using the Nikiforov–Uvarov method for a special case of equal scalar and vector potentials. The energy eigenvalues for bound states and the corresponding wave functions are also obtained in a proper approximation. We have also shown that the results can be used to evaluate the energy eigenvalues of the Yukawa, angle-dependent, and Coulomb potentials. The numerical results are discussed and presented in the table and in the figure, which suggest their applicability to other systems. With the adjusted potential parameters given in the table, it is shown that the interaction of spinless (Klein–Gordon) particles with the Yukawa ring-shaped potential gives positive energy eigenvalues for the various quantum states.

Noboru Kohiyama

The relativistically modified Schrödinger equation is solved for the hydrogen atom for consistency with the eigenvalues of electron’s energy derived from the Dirac equation. Based on the consistency of their eigenvalues, the theory of electromagnetic wave (≥1 mm) emission and absorption by the hydrogen atom is expressed. Another particle in addition to an electron is predicted from this theory.

Jook T. M. Walraven