Hilbert space

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Noun

Hilbert space - a metric space that is linear and complete and (usually) infinite-dimensional

metric space - a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality

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metric space

We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers.

Spatial non-cyclic geometric phase in neutron interferometry by Rauch, Helmut / Journal of Research of the National Institute of Standards and Technology

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