LINEARIZATION OF THE HAMILTONIAN

A procedure is presented for factoring the quadratic Hamiltonian into two terms that are linear in the Hamiltonian. The resulting matrix equations are solved and it is shown that particular solutions lead to the Feshbach-Villars and Dirac equations, as expected. Since there are more matrix equations than unknowns, it would appear that these were the only solutions. However it is shown that there is a continuous set of additional quantum wave equations that have linear Hamiltonians.