Solution of Relativistic Feshbach–Villars Spin-1/2 Equations

We propose a computational method for relativistic spin-1/2 particles by solving the corresponding Feshbach–Villars equation. We have found that the Feshbach–Villars spin-1/2 Hamiltonian can be written as two spin-coupled Feshbach–Villars spin-0 Hamiltonians. For the solution method, we adopted an integral equation formalism. The potential operators are represented in a discrete Hilbert space basis and the relevant Green’s operator has been calculated by a matrix continued fraction.