By Arnold, John Charles
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Extra resources for Ego sum Michael: The origin and diffusion of the Christian cult of St. Michael the Archangel (Ph.D., University of Arkansas, 1997)
RN )dr1 dr1 dr2 . . 18) 40 D. W. 19) where the function g(θ , τ ) is any function that is well-behaved enough for the integral to exist that satisfies the constraints fσ (r, p) = g(θ, τ = 0) = g(θ = 0, τ ) = 1, (g(θ, τ ))∗ = g(−θ, −τ ). 20) The most popular choice, g = 1, corresponds to the Wigner distribution . Quasiprobability distribution functions for many-electron reduced density matrices are computed from very similar formulas. Every kinetic energy density functional is based on some choice, whether implicit or explicit, for the momentum density and/or the quasiprobability distribution function.
Phys Rev A 81:026101 48. Deutsch D (1983) Uncertainty in quantum measurements. Phys Rev Lett 50:631 49. Kraus K (1987) Complementary observables and uncertainty relations. Phys Rev D 35:3070 50. Maassen H, Uffink JBM (1988) Generalized entropic uncertainty relations. Phys Rev Lett 60:1103 51. Reed M, Simon B (1975) Methods of modern mathematical physics, vol II. Academic Press, New York 52. Riesz M (1927) Sur les maxima des formes bilinéaires et sur les fonctionnelles linéaires. Acta Math 49:465 53.
46) by 1 written in the form L2−1/α−1/β . After distributing the powers of L, we arrive at the inequality 1/α R dx[ρ(x)L]α /L 1/β ≤ n(α, β) R β dk[ρ(k)/L] ˜ L . 86) This inequality is not only explicitly dimensionally correct but it also shows its invariance under a change of the unit. 37), we arrive at the uncertainty relation for the continuous Rényi entropies, Sα(x) + Sβ(k) = 1 ln 1−α ≥− R dx[ρ(x)]α Lα−1 + 1 α 1 β ln + ln 1−α π 1−β π 1 2 1 ln 1−β R β 1−β dk[ρ(k)] ˜ L . 88) the uncertainty relation is invariant under a rescaling of the wave function.
Ego sum Michael: The origin and diffusion of the Christian cult of St. Michael the Archangel (Ph.D., University of Arkansas, 1997) by Arnold, John Charles