Many thanks indeed, an exciting discovery! I will proceed immediately to developing these new solutions with Schroedinger quantization in preparation for numerical solution, then add a potential. The quantized versions may be soluble to give completely new relativistic free particle wavefunctions both for translational and rotational free particle motion. The golden age of quantum mechanics always comes up with something new, almost a hundred years after its first development. This is essentially quantization of ECE2 theory. This is of course the method we have used in many previous UFT papers, many variations on a them by Paul Dirac and contemporaries, but always based on geometry so the Dirac equation has become the fermion equation of generally covariant unified field theory (now ECE2 theory).
To: EMyrone@aol.com
Sent: 29/08/2015 11:30:00 GMT Daylight Time
Subj: Exact solution of the relativistic momentum equationIn note 326(4) eq.(33) can be solved with some effort in computeralgebra without approximation v<<c, see attached. There are 4 solutions for p^2, the results differ in signs and a summand m*H1.
Horst
Am 24.08.2015 um 15:57 schrieb EMyrone:
This note uses a Dirac type quantization to produce the equation (21), a relativistic Schroedinger equation which must be solved for the wavefunctions psi. In general this is a highly non trivial procedure which must be carried out numerically in three dimensions. However, it is straightforward to show that this type of quantization produces small shifts in the H atom energy levels given by the expectation value (28). The Thomas factor is given correctly by the Sommerfeld atom, but there is no spin orbit interaction, because the Sommerfeld atom does not contain a spin quantum number, later suggested by the Sommerfeld group itself and developed by Pauli and others. As in previous UFT papers spin orbit coupling and many new effects of development of ECE appears with the use of the SU(2) basis and Pauli matrices. It is known from UFT325 that these orbitals in two dimensions must be the result of a quantization of a two dimensional precessing ellipse, and that will be the subject of the next note. This method is much clearer than that used by Sommerfeld himself in 1913, who did not have the benefit of Schroedinger Debye quantization (circ 1923 / 1924). Sommerfeld produced orbitals in 1913 which he communicated by letter to Einstein.