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The $$\gamma$$ function in quantum theory II. Mathematical challenges and paradoxa
- Source :
- Journal of Mathematical Chemistry. 60:267-282
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- 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.
Details
- ISSN :
- 15728897 and 02599791
- Volume :
- 60
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Chemistry
- Accession number :
- edsair.doi.dedup.....49e92c730bb84e8c33becbf080afe4a1