Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly citedIn quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us to understand either from the viewpoint of the other. Here we show that all general time-dependent solutions of the free-particle Schrodinger equation can be mapped to solutions of the Schrodinger equation for harmonic potentials, both the trapping oscillator and the inverted `oscillator'. This map is fully invertible and therefore induces an isomorphism between both types of system, they are equivalent. A composition of the map and its inverse allows us to map from one harmonic oscillator to another with a different spring constant and different center position. The map is independent of the state of the system, consisting only of a coordinate transformation and multiplication by a form factor, and can be chosen such that the state is identical in both systems at one point in time. This transition point in time can be chosen freely, the wave function of the particle evolving in time in one system before the transition point can therefore be linked up smoothly with the wave function for the other system and its future evolution after the transition point. Such a cut-and-paste procedure allows us to describe the instantaneous changes of the environment a particle finds itself in. Transitions from free to trapped systems, between harmonic traps of different spring constants or center positions, or, from harmonic binding to repulsive harmonic potentials are straightforwardly modelled. This includes some time dependent harmonic potentials. The mappings introduced here are computationally more efficient than either state-projection or harmonic oscillator propagator techniques conventionally employed when describing instantaneous (non-adiabatic) changes of a quantum particle's environmentPeer reviewe

Índices de eficiência reprodutiva de búfalos da Amazônia Oriental do Brasil

Foram avaliados registros de manejo reprodutivo de búfalos das raças Jafarabadi, Murrah, Mediterrâneo, Carabao e Tipo Baio, bem como seus mestiços, no período de 1983 a 2005. Estudaram-se as características reprodutivas: idade à primeira cria (média de 1052,52±120,45 dias), intervalo de partos (média de 399,69±23,78 dias), eficiência reprodutiva (média de 91,09±1,89%), fertilidade real adaptada (média de 29,30±4,40 quilogramas de bezerro parido por ano), produtividade ao primeiro parto adaptada (média de 33,75±6,89 quilogramas) e produtividade acumulada adaptada (média de 22,86±6,55 quilogramas de bezerro parido por ano). Foram verificadas influências do ano de parto e o grau de sangue da fêmea sobre as características estudadas, o que indica que tais efeitos devem ser incluídos na avaliação genética e na seleção dos animais. Os índices produtivos utilizados mostraram-se de grande valia para a seleção, devendo ser mais estudadas suas interações relativas ao desempenho geral do rebanho