TITLE:
The Fourier Transform and Principles of Quantum Mechanics
AUTHORS:
Do Tan Si
KEYWORDS:
Fourier Transform of Bra, Obtaining Dirac Commutation Relation and Principles of Quantum Mechanics
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.4,
April
18,
2018
ABSTRACT: From the hypotheses that the position-representation of a physical state is
the Fourier transform of its momentum-representation and that the timerepresentation
is the inverse Fourier transform of its energy-representation,
we are able to obtain the Planck relation E = hν , the de Broglie relation p = h /λ , the Dirac fundamental commutation relation, the Schr?dinger equations,
the Heisenberg uncertainty principle in quantum mechanics, and the
annihilation/creation of a photon from excitation/de-excitation of an atom
following Bohr.