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Chris Culellar, The University of Texas at El Paso Evan Longpre, The University of Texas at El PasoFollow Vladik Kreinovich, The University of Texas at El PasoFollow
11-2010
Technical Report: UTEP-CS-10-53
To appear in Journal of Uncertain Systems, 2012, Vol. 6, No. 2.
It is known that in quantum mechanics, the set S of all possible states coincides with the set of all the complex-valued functions f(x) for which the integral of |f(x)|2 is 1. From the mathematical viewpoint, this set is a unit sphere in the space L2 of all the functions for which this integralis finite. Because of this mathematical fact, usually the set S is considered with the topology induced by L2, i.e., topology in which the basis of open neighborhood of a state f is formed by the open balls. This topology seem to work fine, but since this is a purely mathematical definition, a natural question appears: does this topology have a physical meaning? In this paper, we show that a natural physical definition of closeness indeed leads to the usual L2-topology.
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Technical Report: UTEP-CS-10-53
To appear in Journal of Uncertain Systems, 2012, Vol. 6, No. 2.