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Understanding geometrical phases in quantum mechanics: An elementary example

  • Part I. Invited Papers Dedicated To Asim Orhan Barut
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Abstract

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 unavoidable breaking of projective symmetry caused by using the Schrödinger equation.

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Authors and Affiliations

  1. Theoretical Division, Los Alamos National Laboratory, 87545, Los Alamos, New Mexico

    J. C. Solem

  2. Department of Physics, University of Texas at Austin, 78712, Austin, Texas

    L. C. Biedenharn

Authors
  1. J. C. Solem
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  2. L. C. Biedenharn
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Additional information

To Professor Asim O. Barut on the occasion of his 65th birthday.

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Solem, J.C., Biedenharn, L.C. Understanding geometrical phases in quantum mechanics: An elementary example. Found Phys 23, 185–195 (1993). https://doi.org/10.1007/BF01883623

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  • DOI: https://doi.org/10.1007/BF01883623

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