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.
 Publication:

Foundations of Physics
 Pub Date:
 February 1993
 DOI:
 10.1007/BF01883623
 Bibcode:
 1993FoPh...23..185S