The numerical methods and results for the special relativistic orbit can be used to solve for the Sommerfeld atom (1913) and Dirac atom (1927 / 1928) without the use of the crude approximations used by Dirac. He made these for the sake of analytical tractability, and they are very rough, the total energy is approximated by the rest energy for example, and it is assumed that U << m c squared. The Dirac equation has been improved into the ECE fermion equation by the AIAS group, removing negative energy and the unobservable Dirac sea. I will proceed to write up my sections of UFT328, and UFT329 will probably deal with the Sommerfeld and Dirac hamiltonians and lagrangians. The former use O(3), the latter use SU(2) and the Pauli matrices, otherwise they are the same before quantization. The early quantization by Bohr and Sommerfeld (1912 to 1913) was replaced by Schroedinger quantization in the early twenties, and that was used by Dirac. They are both theories of special relativistic quantum mechanics. In ECE2, special relativity in one sense is also generally covariant, so the distinction between special and general relativity is no longer needed. The physics all becomes Cartan geometry. The true Sommerfeld orbitals are the quantized versions of the ones that appear in the following postings on this blog, with the gravitational potential between a mass m in orbit around a mass M replaced by the electrostatic potential between proton and electron in the H atom.

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