An eight-component relativistic wave equation for spin-1/2 particles I

An eight-component relativistic wave equation for spin-1/2 particles is derived. It is obtained from a spin-1/2 wave equation, which contains second-order derivatives in both space and time, by a procedure involving the linearization of the time derivative. It is in Hamiltonian form and is analogous to the two-component spin-0 equation, which features the use of an indefinite inner product in the description of the solution space. It is used to produce the relativistic bound-state energy eigenvalue spectrum and wavefunctions for the hydrogen atom. (author)