I went through my calculations again and found that the correct free particle quantization equation is Eq. (29) with gamma defined by Eq. (32) and the de Broglie wave particle dualism by Eq. (33). So these equations can be solved by computer algebra to give E in terms of p sub 0, the classical momentum, and kappa. The cross check on page (5) confirms that everything is self consistent. Having gone through this baseline calculation the particle on a ring and H atom can be defined in a relativistic context. The answer to the computer algebra must be:

E squared = (h bar kappa c) squared + m squared c fourth

so this gives a check on the results of the computer algebra. The fermion equation for the free particle is therefore Eq. (29) where gamma is given by Eq. (32). and where the de Broglie wave particle dualism is given by Eq. (33). Although these equations look like familiar special relativity they are the quantization of the ECE2 Lorentz force equation.