Understanding geometrical phases in quantum mechanics: An elementary example

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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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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Keywords

  • Exact Solution
  • Quantum Mechanic
  • Quantal State
  • Mechanical State
  • Vector Potential