Understanding geometrical phases in quantum mechanics: An elementary example

@article{Solem1993UnderstandingGP,
  title={Understanding geometrical phases in quantum mechanics: An elementary example},
  author={Johndale C. Solem and Lawrence C. Biedenharn},
  journal={Foundations of Physics},
  year={1993},
  volume={23},
  pages={185-195}
}
We discuss an exact solution to the simplest nontrivial example of a geometrical phase in quantum mechanics. By means of this example: (1) we elucidate the fundamental distinction between rays and vectors in describing quantum mechanical states; (2) we show that superposition of quantal states is invalid; only decomposition is allowed—which is adequate for the measurement process. Our example also shows that the origin of singularities in the analog vector potential is to be found in the… 
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