In this article we present a mathematical solution that extends and explores the solution found in chapter 11 of the book "Quantum Mechanics", from "The Feynman Lectures on Physics", about the neutral Kaon. The extension is built within the context of the CP symmetry for the two neutral Kaon decays considered in this chapter: (i) In two Pions, starting in the |K1 state; (ii) In three Pions, from the |K2 state. We found two mathematical expressions that allow to accommodate, separately, each one of the mean lifetime for these decays, unlike the solution given by Feynman that allows to accommodate only one of these mean lifetime. The extended solution is approximate because a small break in CP T symmetry is assumed in these decays; however, it has the advantage of avoiding the colloquially commented situation by Feynman of remaining "forever" from the neutral Kaon in the |K2 state in the situation in which the only possible decay channel was in two Pions. keywords: Neutral K meson, CP and CP T symmetry, Decay of the neutral Kaon into three Pions.
We solve the inverse problem corresponding to the fundamental problem of the classical dynamics of a material particle through a matrix treatment: assuming knowing the mass and the position (the trajectory, in relation to an inertial reference) of a particle at all times, we impose that this corresponds to the eigenvector of a “position matrix". Subsequent development leads to a “force matrix", which has the resultant force on the particle as its eigenvector. We identified some limitations of this matrix treatment.
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