We proposed the concept of reciprocal wave function which is interpreted as the relative non-finding probability amplitude that represents the physical reality in a probabilistic way, like the wave function does. In this note we explore a further question which arises naturally: Why this novel form of probability description of physical reality could exist in quantum theory.
PDF (This a new version of the previous work.)
A review report on our paper was received last week. For some unexpected reasons, it is the only peer-review report which we have received for nearly two years.
In seminars initiated by us, we always highlighted some interesting points at the beginnings: the failure of the classical nonfinding probability; the unprovablity for the postulates in quantum physics, etc.
Thus，after submitting the response, we decide to update the reply here (a title added), and hope it can be helpful for the readers who may be interested in the paper.
The reciprocal wave function was introduced into quantum mechanics, and it was asserted that this wave function describes the physical reality. In this note we shall show, from the more general standpoint, why this novel description of the physical reality exists.
It is shown that the correction to the vertex for fermion pair annihilation and production in the low-energy region is equal to the value of the wave function for the two-body system at the origin. The procedure also shows directly that the emergence of the Sommerfeld effect in quantum mechanics is the product of the reduction of the vertex correction from four spacetime dimensions to three-dimensional space. Meanwhile, the reciprocal wave function is introduced into quantum mechanics.