Portrait of Albert Einstein wearing glasses Portraits Men

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Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Albert Einstein with unidentified group; City College, New York Portraits Groups; Men

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Portrait of Albert Einstein in tempera (black and white) on cardboard Artworks

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Albert Einstein sailing with Margarete Lebach; Huntington Portraits; Couples

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Albert and Elsa Einstein seated on ship deck Portraits; Couples

Signed lower right Albert Einstein

Albert Einstein with Coriolano Alberini and unidentified men; Buenos Aires, Argentina Portraits Groups; Men

Dedication: Al Prof. Alberto Einstein, maestro y amigo, signed Coriolano Alberini, Dean of the Faculty of Philosophy and Literature of the University of Buenos Aires

Albert Einstein, Paul Langevin, Princesse de Noeille, and Paul Painleve; Paris Portraits Groups

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Albert Einstein with unidentified group Portraits Groups

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Albert Einstein with Robert Andrews Millikan, Albert Michelson and unidentified men; Pasadena, California Portraits Groups; Men

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Albert Einstein and unidentified man Portraits Groups; Men

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Albert Einstein's Weekend Home; Caputh, near Berlin Architecture; Residences; Exterior

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Deck; Albert Einstein's Weekend Home; Caputh, near Berlin Architecture; Residences; Exterior

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Study; Albert Einstein's Weekend Home; Caputh, near Berlin Architecture; Residences; Interior

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