Kobe, D. H.Aguileranavarro, V. C.2014-05-202014-05-201994-08-01Physical Review A. College Pk: American Physical Soc, v. 50, n. 2, p. 933-938, 1994.1050-2947http://hdl.handle.net/11449/32348A derivation from first principles is given of the energy-time uncertainty relation in quantum mechanics. A canonical transformation is made in classical mechanics to a new canonical momentum, which is energy E, and a new canonical coordinate T, which is called tempus, conjugate to the energy. Tempus T, the canonical coordinate conjugate to the energy, is conceptually different from the time t in which the system evolves. The Poisson bracket is a canonical invariant, so that energy and tempus satisfy the same Poisson bracket as do p and q. When the system is quantized, we find the energy-time uncertainty relation DELTAEDELTAT greater-than-or-equal-to HBAR/2. For a conservative system the average of the tempus operator T is the time t plus a constant. For a free particle and a particle acted on by a constant force, the tempus operators are constructed explicitly, and the energy-time uncertainty relation is explicitly verified.933-938engArtigo10.1103/PhysRevA.50.933WOS:A1994PB59200011Acesso restritoWOSA1994PB59200011.pdf