A quantum mechanical proof of the fourier inversion formula


  • Nelson Castro Universidade Federal da Paraíba.
  • Ramón Mendoza Universidade Federal de Pernambuco.
  • Jacqueline F. Rojas Universidade Federal da Paraíba.




Fourier transform, Position operator, Momentum operator, , Extension.


The translation of the observable, position and momentum, of a given particle in the real line, at a certain time t, from Classical Mechanics, into the operators, position and momentum, in Quantum Mechanics, gives us the inspiration to make a proof of the existence of the Fourier's Inverse Transform, using algebraic relations involving these operators (position and momentum), a few of Linear Algebra and Analysis, without resorting to the classical technics like Fubini's Theorem and Lebesgue's Dominated Convergence Theorem.


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How to Cite

N. Castro, R. Mendoza, and J. F. Rojas, “A quantum mechanical proof of the fourier inversion formula”, Proyecciones (Antofagasta, On line), vol. 30, no. 3, pp. 441-457, Dec. 2011.