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Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions. Symmetry (Basel) 2017. [DOI: 10.3390/sym9100217] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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Galapon EA. Theory of quantum arrival and spatial wave function collapse on the appearance of particle. Proc Math Phys Eng Sci 2008. [DOI: 10.1098/rspa.2008.0278] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The unexpected connection is unravelled between the collapse of the wave function on the appearance of particle and the quantum time-of-arrival problem in one dimension. To do so, a theory of quantum first time of arrival is developed in the interacting case for arbitrary arrival point in one dimension based on a self-adjoint and canonical coarse graining of a time-of-arrival operator that derives the classical time-of-arrival observable. The appearance of particle in quantum mechanics is then considered in the light of this theory. It is found that the appearance of particle arises as a combination of the collapse of the initial wave function into one of the eigenfunctions of the time-of-arrival operator, followed by a unitary Schrödinger evolution of the eigenfunction.
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Affiliation(s)
- Eric A Galapon
- Theoretical Physics Group, National Institute of Physics, University of the Philippines DilimanQuezon City 1101, The Philippines
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