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While the square root of Dirac’s    $$\delta$$  δ is not defined in any standard mathematical formalism, postulating its existence with some further assumptions defines a generalized function called    $$\gamma (x)$$  γ ( x ) which permits a quasi-classical treatment of simple systems like the H atom or the 1D harmonic oscillator for which accurate quantum mechanical energies were previously reported. The so-defined    $$\gamma (x)$$  γ ( x ) is neither a traditional function nor a distribution, and it remains to be seen that any consistent mathematical approaches can be set up to deal with it rigorously. A straightforward use of    $$\gamma (x)$$  γ ( x ) generates several paradoxical situations which are collected here. The help of the scientific community is sought to resolve these paradoxa.

The $$\gamma$$ function in quantum theory II. Mathematical challenges and paradoxa