THE NEGATIVE ENERGY EIGENVALUES OF THE DIRAC EQUATION SUBJECT TO A COULOMB POTENTIAL

This paper solves the eigenvalues of the bound states of the Dirac equation when there is a Coulomb potential in its Hamiltonian. In the literature, only a positive energy spectrum is solved for this Hamiltonian, which is less than the rest energy and describes the bound states. The author calls it positive energy solutions. In this paper, we show that there are negative energy solutions in addition. The positive and negative energy eigenvalues are one-to-one correspondence and just contrary numbers to each other, which is called the symmetry with respect to the positive and negative eigenvalues. The present work shows that the Dirac equation with a Coulomb potential has symmetry of positive and negative eigenenergy values for both the bound states and unbound states.