Resumo

CASTRO, Nelson N. de O; ROJAS, Jacqueline  e  MENDOZA, Ramon. A Quantum Mechanical Proof of the Fourier Inversion Formula. Proyecciones (Antofagasta) [online]. 2011, vol.30, n.3, pp. 441-457. ISSN 0716-0917.  doi: 10.4067/S0716-09172011000300010.

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.

Palavras-chave : Fourier transform; position operator; momentum operator; extension.