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3-Heisenberg-Robertson-Schrodinger Uncertainty Principle
Version 1
: Received: 19 October 2024 / Approved: 23 October 2024 / Online: 25 October 2024 (09:47:16 CEST)
How to cite: KRISHNA, K. M. 3-Heisenberg-Robertson-Schrodinger Uncertainty Principle. Preprints 2024, 2024101900. https://doi.org/10.20944/preprints202410.1900.v1 KRISHNA, K. M. 3-Heisenberg-Robertson-Schrodinger Uncertainty Principle. Preprints 2024, 2024101900. https://doi.org/10.20944/preprints202410.1900.v1
Abstract
Let X be a 3-product space. Let A : D(A) ⊆ X → X , B : D(B) ⊆ X → X and C : D(C) ⊆ X → X be possibly unbounded 3-self-adjoint operators. Then for all x ∈ D(ABC) ∩ D(ACB) ∩ D(BAC) ∩ D(BCA) ∩ D(CAB) ∩ D(CBA) with ⟨x, x, x⟩ = 1, we show that (1) ∆x(3, A)∆x(3, B)∆x(3, C) ≥ |⟨(ABC − aBC − bAC − cAB)x, x, x⟩ + 2abc|, where ∆x(3, A) := ∥Ax − ⟨Ax, x, x⟩x∥, a := ⟨Ax, x, x⟩, b := ⟨Bx, x, x⟩, c := ⟨Cx, x, x⟩. We call Inequality (1) as 3-Heisenberg-Robertson-Schrodinger uncertainty principle. Classical HeisenbergRobertson-Schrodinger uncertainty principle (by Schrodinger in 1930) considers two operators whereas Inequality (1) considers three operators.
Keywords
Uncertainty Principle; Banach space
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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