Simulação óptica de uma partícula livre quântica relativística
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2016-03-22
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Universidade Federal de Goiás
Resumo
Among the first attempts towards the unification of quantum and special relativity theories
that which more highlighted was the Dirac’s electron theory. Amongst its achievements is the
accurated calculation of the hydrogen spectrum and the antiparticles prediction. Even though
it provides good results, some difficulties arise in this theory such as the existence of negative
energy states for free particles. At the same time that it allows for the antiparticle discovery, it
leads to questions like the trembling motion of a free electron (zitterbewegung). It is not a
consensus whether this motion is real or just a theoretical failure in describing the reality. In
this work we present a proposal to simulate the Dirac electron dynamics and, therefore,
zitterbewegung, by means of a transformation of a paraxial light beam. The same
transformation as is carried out on the vector state by the Dirac’s evolution operator is
implemented in the transverse beam profile using wave plates and spatial light modulator. The
proposal includes the cases of one and two spatial dimensions by simulating the spatial
degrees of freedom into the transverse coordinates of the light beam, which offers a difficulty
in simulating the three dimensional dynamics in general case. However, we show that it is
possible for particular initial states. Our simulation presents some advantages over previously
ones, namely: it does not require the construction of specificaly designed devices; the
adjustable parameters are present on phases printed by the modulator and can be arbitrarily
changed; it permits the measurement of the mean as well as the standard position operators;
it permits the simulation in two and three spatial dimensions.
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SILVA, Thais L. Simulação óptica de uma partícula livre quântica relativística. 2016. 92 f. Dissertação (Mestrado em Fisica) - Universidade Federal de Goiás, Goiânia, 2016.