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NeuroQuantology

Evolution of Schrödinger Uncertainty Relation in Quantum Mechanics

Andrew Angelow

Published Feb 3, 2009• 4 citations
Publisher

Abstract

In the present article, we discuss one of the basic relations of Quantum Mechanics – the Uncertainty Relation (UR). In 1930, few years after Heisenberg, Erwin Schrodinger generalized the famous Uncertainty Relation in Quantum Mechanics, making it more precise than the original. The present study discusses recent generalizations of Schrodinger’s work and explains why his paper remains almost forgotten in the last century.

DOI
10.14704/nq.2009.7.2.235

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In the present article, we discuss one of the basic relations of Quantum Mechanics – the Uncertainty Relation (UR). In 1930, few years after Heisenberg, Erwin Schrodinger generalized the famous Uncertainty Relation in Quantum Mechanics, making it more precise than the original. The present study discusses recent generalizations of Schrodinger’s work and explains why his paper remains almost forgotten in the last century.
The original Schrödinger’s paper is translated and annotated in honour of the 70 −th anniversary of his Uncertainty Relation [will appear in Bulg.J.Phys.]. In the annotation it is shown that the Uncertainty Relation can be written in a complete compact canonical form. ANNOTATION by A. Angelow ++, M.-C. Batoni +++ The main reason to publish the original Schrödinger’s paper in English, is the fact that no one of the books on Quantum Mechanics cites it (see for example [1 †-15 †]). Actually, Schrödinger’s paper is chiefly based on the notes of the seminars of Physics-Mathematical Section of The Prussian Academy, where many famous physicists worked to establish the underlying basis of Quantum Theory. Being a kind of internal report, this work remained, for many years at a certain marginal distance from the physicist scientific awareness. Another argument in favour of its oblivion concerns the enthusiastic discussions, mostly about the physical interpretation of the uncertainty principle, rather than its mathematical straightforward derivation. After Schrödinger, the very first appearance of the new uncertainty
In the present article, we discuss two types of uncertainty relations in Quantum Mechanics–multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schrödinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics–Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.
In the present article, we discuss two types of uncertainty relations in Quantum Mechanics–multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schrödinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics–Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.
100±Δt100\pmΔt100±Δt Years of Quantum Uncertainty: From Origins to Modern Insights
Heisenberg's uncertainty principle is a cornerstone of quantum mechanics, marking a decisive departure from classical physics. Conceived almost a century ago through a thought experiment showing that measuring an electron's position inevitably disturbs its momentum, it began as a deceptively simple idea that sparked countless studies and grew into the rich research field it is today. This review traces its development into a spectrum of mathematical formulations -- known as uncertainty relations -- and explores their interconnections and wide-ranging applications. We highlight its central role in quantum metrology, where it underpins strategies for extracting information from quantum systems with ever-increasing precision, and its links to multiparameter estimation and squeezed states. This review, dedicated to the centenary of the uncertainty principle, reflects on how it has deepened our understanding of quantum theory and driven practical advances, and looks ahead to a century poised for further surprising and transformative discoveries.