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An operator for simultaneous unsharp measurement of coordinate and momentum
Author(s) -
Davidović D.M.,
Arsenović D.
Publication year - 2003
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200310008
Subject(s) - orthonormal basis , operator (biology) , eigenvalues and eigenvectors , mathematics , position and momentum space , momentum operator , lattice (music) , orthonormality , momentum (technical analysis) , position operator , phase space , mathematical analysis , pure mathematics , physics , ladder operator , compact operator , quantum mechanics , quasinormal operator , computer science , finite rank operator , repressor , banach space , chemistry , acoustics , biochemistry , transcription factor , programming language , finance , economics , extension (predicate logic) , gene
Starting from a complete but not overcomplete set of coherent states defined on a lattice in the phase space, we construct the orthonormal basis using the procedure due to Lödwin, in which all states to be normalized enter the procedure on equal footing. We show that our normalized states may be interpreted as eigenstates of the operator of simultaneous unsharp measurement of coordinate and momentum. In a sense we followed the classical idea of von Neumann but without drawbacks which in his construction of such an operator were due to the use of the Gram‐Schmidt orthonormalization procedure which is somewhat inappropriate for this purpose. We discuss the obtained results.