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Coordinate formalism on Hilbert manifolds: string bases of eigenvectors

Kryukov, Alexey (2002) Coordinate formalism on Hilbert manifolds: string bases of eigenvectors. [Preprint]

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    Abstract

    Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov}, \cite{Kryukov1} is further analyzed. The main subject here is a comparison of the ordinary and the string bases of eigenvectors of a linear operator as introduced in \cite{Kryukov}. It is shown that the string basis of eigenvectors is a natural generalization of its classical counterpart. It is also shown that the developed formalism forces us to consider any Hermitian operator with continuous spectrum as a restriction to a space of square integrable functions of a self-adjoint operator defined on a space of generalized functions. In the formalism functional coordinate transformations preserving the norm of strings are now linear isometries rather than the unitary transformations.


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    Item Type: Preprint
    Keywords: Hermitian operators, self-adjoint operators, generalized eigenvalue problem
    Subjects: Specific Sciences > Physics > Quantum Mechanics
    Depositing User: Alexey Kryukov
    Date Deposited: 15 Mar 2002
    Last Modified: 07 Oct 2010 11:10
    Item ID: 580
    URI: http://philsci-archive.pitt.edu/id/eprint/580

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