Do Tan, S. (2019) Advances in Optics, Chapter 5. In: The Fourier Transform Relation between m Dirac bras < k^→|=FT< r^→| and Wave Optics, Reviews Book Series, Volume 4, International Frequency Sensor Association Publishing, Barcelona.

has been cited by the following article:

• TITLE: Principles of Quantum Mechanics and Laws of Wave Optics from One Mathematical Formula

  AUTHORS: Do Tan Si

  KEYWORDS: Fourier Transform in Quantum Mechanics, Permutation Relations between Operators, Laws of Wave Optics, Diffractions by Multiform Identical Objects

  JOURNAL NAME: Applied Mathematics, Vol.10 No.11, November 11, 2019

  ABSTRACT: Finding that in the formula of expansion of a function into a series of wave-like functions the coefficients are its Fourier transforms, if existed, we deduce mathematically all the principles and hypothesis that illustrated physicists utilized to build quantum mechanics a century ago, beginning with the duality particle-wave principle of Planck and including the Schrödinger equations. By the way, we find a simple Fourier transform relation between Dirac momentum and position bras and a useful permutation relation between operators in phase and Hilbert spaces. Moreover, from the found particle-wave duality formula we prove and obtain again essentially by mathematical analysis all the laws of wave optics concerning reflections, refractions, polarizations, diffractions by one or many identical 3D objects with various forms and dimensions.