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This project aims to study the non-relativistic quantum systems of two, four and eight energy levels that describe particles with spin s=1/2 in external elds and interacting with each other. We nd exact analitical solutions for these systems. Such systems have extensive applications in various areas of physics, among which its possible to highlight quantum computing. Possible applications of the results are the construction of quantum universal logic gates.These quantum logic gates are an essential element in the development of so-called quantum computers. The analysis and implementation of quantum computers requires handling systems of various levels, subject to time-dependent external elds. This work presents a solution to the so-called Rabi problem, a particular problem at two levels. An example of a solution to the system of four levels, related to two spins problem is also investigated. We obtained exact solutions for systems of eight levels with possible application to the Quantum Error Correction.

A evolução temporal de sistemas de spins 1/2 congelados no espaço e descritos pelo modelo de Heisenberg