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- W2316741646 abstract "We present a N -dimensional quantization a la Berezin-Klauder or frame quantization of the complex plane based on overcomplete families of states (coherent states) generated by the N first harmonic oscillator eigenstates. The spectra of position and momentum operators are finite and eigenvalues are equal, up to a factor, to the zeros of Hermite polynomials. From numerical and theoretical studies of the large N behavior of the product λM (N)λm(N) of largest and non null smallest positive eigenvalues, we infer the inequality ∆N (Q) δN (Q) = σN < → N→∞ 2π (resp. ∆N (P ) δN (P ) = σN < → N→∞ 2π) involving, in suitable units, the maximal (∆N (Q)) and minimal (δN (Q)) sizes of regions of space (resp. momentum) which are accessible to exploration within this finite-dimensional quantum framework. Interesting issues on the measurement process are discussed. Pacs03.65.Bz, 03.65.Ca" @default.
- W2316741646 created "2016-06-24" @default.
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- W2316741646 date "2004-11-30" @default.
- W2316741646 modified "2023-09-27" @default.
- W2316741646 title "Finite dimensional quantizations of the particle motion: toward new space and momentum inequalities?" @default.
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