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The function in quantum theory II. Mathematical challenges and paradoxa
Zs É Mihálka1,2, M Nooijen3, Á Margócsy1,2
1Institute of Chemistry, Laboratory of Theoretical Chemistry, ELTE Loránd Eötvös University, P.O.B. 32, Budapest 112, 1518 Hungary.
Journal of Mathematical Chemistry
|February 28, 2022
Summary
Researchers postulate a generalized function, the square root of Dirac
Area of Science:
- Theoretical Physics
- Quantum Mechanics
- Mathematical Physics
Background:
- The square root of Dirac's delta function is not formally defined in standard mathematical frameworks.
- Existing quantum mechanical treatments provide accurate energies for systems like the H atom and 1D harmonic oscillator.
Purpose of the Study:
- To explore the implications of a postulated generalized function, the square root of Dirac's delta function.
- To investigate its potential for quasi-classical treatments of quantum systems.
- To identify and collect paradoxical situations arising from its use.
Main Methods:
- Postulating the existence of the square root of Dirac's delta function.
- Applying this generalized function to simple quantum systems (H atom, 1D harmonic oscillator).
- Analyzing the resulting mathematical and physical implications.
Main Results:
- A generalized function, termed the square root of Dirac's delta function, has been defined.
- This function allows for a quasi-classical treatment of specific quantum systems.
- The application of this function leads to paradoxical situations.
Conclusions:
- The defined square root of Dirac's delta function is a novel mathematical entity, distinct from traditional functions or distributions.
- Rigorous mathematical frameworks for its consistent treatment are yet to be established.
- Further scientific community input is required to resolve the identified paradoxa.
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