Related Experiment Video
Updated: Oct 2, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
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.
Abstract:
While the square root of Dirac's is not defined in any standard mathematical formalism, postulating its existence with some further assumptions defines a generalized function called 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 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 generates several paradoxical situations which are collected here. The help of the scientific community is sought to resolve these paradoxa.
Related Concept Videos
The Uncertainty Principle
The Quantum-Mechanical Model of an Atom
The Pauli Exclusion Principle
Parseval's Theorem
Interestingly, Parseval's theorem also holds for the trigonometric form of the Fourier series, which...
The de Broglie Wavelength
The Bohr Model

