Abstract
The analogy between the classical dynamics of a system of N harmonic oscillators and the quantum mechanics of a system with N orthogonal quantum states is discussed in the context of geometric phases. The analogy between the quantum mechanical description of a spin 1/2 system and the description of the polarization behavior of light by Jones calculus, along with the geometric descriptions known as the Bloch sphere and the Poincare sphere are described. Finally, the elements of a more general calculus capable of handling mixed evolution of light beams in the propagation direction and polarization by means of 3×3 matrices and its usefulness in the interpretation of geometric phase experiments in optics are described.
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