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If you introduce new premises, the maths are not the same. For my example above, I have introduced the phase velocity of the wave equalling the particle velocity. That does not occur in any book or paper on QM of which I am aware, apart from anything I have written, such as the above. What it does is provide a method for calculating properties that standard theory can not dowiht0put introducing "validation corrections" (See Pople's Noble lecture).