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About Heisenberg Uncertainty Relation

Erwin Schrödinger

Published Jan 1, 1930• 97 citations

Abstract

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

Related papers

About Heisenberg Uncertainty Relation (by E.Schrodinger)

A. Angelow, M. C. Batoni

The original Schrodinger's paper is translated and annotated in honour of the 70-th anniversary of his Uncertainty Relation [published also in: Bulg. Journal of Physics,vol.26,no.5/6 (1999) pp.193-203]. In the annotation it is shown that the Uncertainty Relation can be written in a complete compact canonical form.

arXiv:quant-ph/9903100•Mar 30, 1999•29 citations

A brief review on uncertainty principle and its variants

Manas Protim Saikia

In this paper, using two different formulations, we attempted to first provide an overview of mathematical interpretations of Heisenberg's uncertainty principle. This was done in order to emphasise the mathematical justification for the uncertainty principle's existence. First, we went over in detail the matrix formulation found in Schrodinger's original paper on uncertainty. Next, we reviewed the mathematical proof of the uncertainty principle in a Fourier series formulation and examined the results. We attempted to provide a comprehensive overview of the modified forms of the uncertainty relation in the Quantum Gravitational, Relativistic, and Entropic domains along with other variants after realizing that the most well-known uncertainty relation is not universal. All of these concepts also demonstrate a great deal of potential for use in the emerging new technologies. Our goal was to gather all of these dispersed variations of the uncertainty principle in one location. The current state of these theories, as well as their applications and limitations, are thoroughly discussed.

Journal of Advanced Education and Sciences•Jan 1, 2026•0 citations

Evolution of Schrödinger Uncertainty Relation in Quantum Mechanics

Andrew Angelow

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.

NeuroQuantology•Feb 3, 2009•4 citations

Evolution of Schrodinger Uncertainty Relation in Quantum Mechanics

Andrey K. Angelow

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.

arXiv:0710.0670•Oct 2, 2007•1 citation

Quantum Mechanics and the Heisenberg Uncertainty Principle

Robert Shanafelt

This paper is an annotated bibliography of popular works on quantum mechanics and the Heisenberg uncertainty prinicple written by physicsts. The writings of 30 physicists are represented, beginning with the works of founders such as Planck, Einstein, Bohr, and Heisenberg, and ending with those of such contemporary figures as David Bohm, John S. Bell, Roger Penrose, and Stephen Hawking. In addition to the bibliographic annotations, this paper also includes an introduction, a brief historical review, and a description of importance dictionary, encyclopedia, and Internet resources.

Science & Technology Libraries•Jun 21, 1995•0 citations

Foundations of Physics (Critical View): Quantum Mechanics

Sergey N. Artekha

The proposed book consists of two parts and is devoted to the systematic analysis of quantum mechanics and the modern theory of electromagnetic phenomena. Some inaccuracies of the application of mathematics in theoretical physics are discussed. This first part examines in detail the basic concepts of quantum mechanics, its apparatus, methods and applications and demonstrates their groundlessness, and often the internal inconsistency of the most common version of the Copenhagen interpretation of quantum mechanics. The book contains a critical analysis of the experiments underlying this theory. All this together proves that the generally accepted version of quantum mechanics is a temporary construction, and the creation of a new consistent theory of the microcosm is required. The book also discusses some alternative ideas applicable to the microcosm. This book may be useful for students, postgraduates, teachers, scientific and technical workers and anyone interested in the basics of physics. To the English version of the book. This is an English translation of the Russian version of the book. Quotations were also translated from Russian-language publications (therefore, for English-language works they are not a literal original, but they convey the essence of the quotations). However, references to pages or chapters have been corrected for the indicated English-language sources.

•Apr 15, 2023•0 citations

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 this paper, using two different formulations, we attempted to first provide an overview of mathematical interpretations of Heisenberg's uncertainty principle. This was done in order to emphasise the mathematical justification for the uncertainty principle's existence. First, we went over in detail the matrix formulation found in Schrodinger's original paper on uncertainty. Next, we reviewed the mathematical proof of the uncertainty principle in a Fourier series formulation and examined the results. We attempted to provide a comprehensive overview of the modified forms of the uncertainty relation in the Quantum Gravitational, Relativistic, and Entropic domains along with other variants after realizing that the most well-known uncertainty relation is not universal. All of these concepts also demonstrate a great deal of potential for use in the emerging new technologies. Our goal was to gather all of these dispersed variations of the uncertainty principle in one location. The current state of these theories, as well as their applications and limitations, are thoroughly discussed.

This paper is an annotated bibliography of popular works on quantum mechanics and the Heisenberg uncertainty prinicple written by physicsts. The writings of 30 physicists are represented, beginning with the works of founders such as Planck, Einstein, Bohr, and Heisenberg, and ending with those of such contemporary figures as David Bohm, John S. Bell, Roger Penrose, and Stephen Hawking. In addition to the bibliographic annotations, this paper also includes an introduction, a brief historical review, and a description of importance dictionary, encyclopedia, and Internet resources.

The proposed book consists of two parts and is devoted to the systematic analysis of quantum mechanics and the modern theory of electromagnetic phenomena. Some inaccuracies of the application of mathematics in theoretical physics are discussed. This first part examines in detail the basic concepts of quantum mechanics, its apparatus, methods and applications and demonstrates their groundlessness, and often the internal inconsistency of the most common version of the Copenhagen interpretation of quantum mechanics. The book contains a critical analysis of the experiments underlying this theory. All this together proves that the generally accepted version of quantum mechanics is a temporary construction, and the creation of a new consistent theory of the microcosm is required. The book also discusses some alternative ideas applicable to the microcosm. This book may be useful for students, postgraduates, teachers, scientific and technical workers and anyone interested in the basics of physics. To the English version of the book. This is an English translation of the Russian version of the book. Quotations were also translated from Russian-language publications (therefore, for English-language works they are not a literal original, but they convey the essence of the quotations). However, references to pages or chapters have been corrected for the indicated English-language sources.