The basis of quantum mechanics' compatibility with relativity--whose\n impairment gives rise to the Klein-Gordon and Dirac equations

Solitary-particle quantum mechanics' inherent compatibility with special\nrelativity is implicit in Schroedinger's postulated wave-function rule for the\noperator quantization of the particle's canonical three-momentum, taken\ntogether with his famed time-dependent wave-function equation that analogously\ntreats the operator quantization of its Hamiltonian. The resulting formally\nfour-vector equation system assures proper relativistic covariance for any\nsolitary-particle Hamiltonian operator which, together with its canonical\nthree-momentum operator, is a Lorentz-covariant four-vector operator. This, of\ncourse, is always the case for the quantization of the Hamiltonian of a\nproperly relativistic classical theory, so the strong correspondence principle\ndefinitely remains valid in the relativistic domain. Klein-Gordon theory\nimpairs this four-vector equation by iterating and contracting it, thereby\ninjecting extraneous negative-energy solutions that are not orthogonal to their\npositive-energy counterparts of the same momentum, thus destroying the basis of\nthe quantum probability interpretation. Klein-Gordon theory, which thus depends\non the square of the Hamiltonian operator, is as well thereby cut adrift from\nHeisenberg's equations of motion. Dirac theory confuses the space-time symmetry\nof the four-vector equation system with such symmetry for its time component\nalone, which it fatuously imposes, thereby breaching the strong correspondence\nprinciple for the free particle and imposing the starkly unphysical\nmomentum-independence of velocity. Physically sensible alternatives, with\nexternal electromagnetic fields, to the Klein-Gordon and Dirac equations are\nderived, and the simple, elegant symmetry-based approach to antiparticles is\npointed out.\n