Three-body problem in 3D space: ground state, (quasi)-exact-solvability

We study aspects of the quantum and classical dynamics of a $3$-body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions in the space of relative motion which are functions of mutual distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories in the classical case are of this type. The quantum (and classical) system for which these states are eigenstates is found and its Hamiltonian is constructed. It corresponds to a three-dimensional quantum particle moving in a curved space with special metric. The kinetic energy of the system has a hidden $sl(4,R)$ Lie (Poisson) algebra structure, alternatively, the hidden algebra $h^{(3)}$ typical for the $H_3$ Calogero model. We find an exactly solvable three-body generalized harmonic oscillator-type potential as well as a quasi-exactly-solvable three-body sextic polynomial type potential; both models have an extra integral.Comment: 24 pages, Appendix about non-equal masses adde

¿Qué contiene una escuela? sobre el sentido ético-político de la convivencia escolar

¿Qué contiene una escuela? no es, precisamente, una pregunta simple. Una forma casi ingenua de dar respuesta a la misma nos puede conducir a un proceso de enumeración, por ejemplo, decir que contiene estudiantes, maestros, pupitres, pizarrones, libros. Si, libros y una vez más estaríamos frente a la cuestión anterior. Pero en este caso avocados solamente a uno de los sentidos del término “contener”, esto es, comprender, abarcar. ¿Qué contiene una escuela? implica, también, entre otras acciones sujetar, aguantar, apoyar, acompañar. El interés en este escrito no es el de presentar una serie de prescripciones en torno a lo que debe contener la escuela y qué modelo de convivencia se puede deducir de dichas preceptos. Se ha optado por buscar apoyo en relatos de experiencias de estudiantes y maestros para construir con ellos una mirada comprensiva del sentido político de la convivencia escolar. Muchas de las cosas que aquí se expresan son tan corrientes que pasan por inadvertidas, otras lo son mucho menos. Desde unas y otras, el objetivo principal de este escrito es mostrar que lo que una escuela orientada a la formación de valores ciudadanos contiene no va más allá de lo que sus actores están dispuestos a reconocerle, la manera como dotan de sentido de sus experiencias cotidianas, sus formas de participación, sus decisiones vitales, el apoyo que cada quien recibe y está dispuesto a darle a los otros

a spatial analysis

The cultivation of coca (Erythroxylon coca) in Colombia represents the first step of the largest illegal agribusiness that exists in the world, namely Cocaine. In this production chain, the small local cultivators consists of the first step, followed by the step, where most of the money profit is made. This sphase correspond to the elaboration of cocaine and its commercialization at a global scale which is in the hands of illegal armed groups and drug dealers. Most of the literature related to illicit crops considers the national and global factors that influence the expansion of these products. However, only little is written in the scientific literature concerning the local conditions where the social-environmental impacts due to these activities are concentrated. This study analyses for the first time the local factors (social, economic, environmental and institutional) associated to the expansion of cocaine during the last decade and how these activities have provided the favourable settings for the increase of deforestation in zones of high environmental importance. For the proposed analysis a social-ecological conceptual framework was made, based on literature reviews which were confirmed by statistical analysis of data at a municipal level and the use of bivariate Local Indicators of Spatial Association (LISA) during the two year period of this study. This has allowed an improved comprehension of the complexity between the coca cultivations and its association with the emergence of social-environmental conflicts. It is shown that an relationship exists between deforestation of primary forest in low-laying areas and the increase of cultivated areas of coca with an intensification of land-use conflicts. This study demonstrates the environmental, institutional and social-economical resemblances that determine the establishment of coca cultivations at a local level and its relationship with increase of coca cultivations towards the north and southwest of Colombia and as such the expansion of the social-environmental conflicts