Por qué y cómo encontramos funciones de matrices: entropía en mecánica cuántica

Abstract

Finding matrix functions is a common occurrence in modern day research. The basic analytic method to calculate matrix functions is based in the existance of the generalized Jordan --- or normal --- form of the argument matrix; usually, this method is tedious or hard to follow. In this report we present the typical generalized Jordan form method and an alternative method, which is simpler and usable for smooth functions that accept a Taylor series expansion. As extra-value, we apply the method finding the entropy of a three-level system interacting with a quantized single-mode radiation field.