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 CPT 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.

In this paper, we consider one mathematical extension for the concept NMR pseudo-pure matrix in the particular case of 4 × 4 matrices, from non-physical matrices. Examples of entangled density matrices are presented. Those entanglement, identified by the Peres-Horodecki criterion, is spurious because it is not possible to assign these matrices to any physical state of a system of NMR nuclear spins.

En este artículo consideramos una extensión matemática para el concepto de matriz seudopura RMN, en el caso particular de matrices 4 × 4, a partir de matrices no físicas. Se presentan ejemplos de matrices densidad entrelazadas son presentados. Aquel entrelazamiento, identificado por el criterio de Peres-Horodecki, es espurio debido a que no es posible asignar estas matrices a cualesquiera estados cuánticos de un sistema de espines nucleares RMN.

In this paper we calculate in detail the quantum mechanical propagator for two physical systems, a two-dimensional free particle and a particle in the Earth's gravitational field, according to Feynman sum-over-paths postulate. The method of propagator calculation that we have used is based on an approximation by polynomials, which is consistent with Weierstrass theorem. The results obtained with this method, except for a numerical factor that depend only on the degree of the polynomials, are equal to those obtained through the use of formal methods.

En este artículo calculamos detalladamente el propagador mecánico cuántico para dos sistemas físicos, una partícula libre en dos dimensiones y una partícula en el campo gravitacional de la Tierra, de acuerdo con el postulado de sumas sobre caminos de Feynman. El método de cálculo del propagador que hemos utilizado está basado en una aproximación por polinomios, que es consistente con el teorema de Weierstrass. Los resultados obtenidos con este método, a excepción de un factor numérico que depende solamente del grado de los polinomios, son iguales a aquellos obtenidos con el uso de métodos formales.