Significance of Loewner’s Theorem in the Quantum Theory of Collisions

Wigner, E. P.; von Neumann, J.

doi:10.1007/978-3-662-02781-3_34

E. P. Wigner² &
J. von Neumann²

Part of the book series: The Collected Works of Eugene Paul Wigner ((2875,volume A / 1))

2217 Accesses

Abstract

It can be shown¹ that under rather general conditions one can define “components” of the quantum mechanical wave function of a collision system between which relations of the form

EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaBa % aaleaacaWG2baabeaakiabg2da9maaqaeabaWaaSbaaSqaaiabeY7a % Tbqabaaabeqab0GaeyyeIuoakiaadkfadaWgaaWcbaGaamODaiabeY % 7aTbqabaGccaWGKbWaaSbaaSqaaiabeY7aTbqabaaaaa!43A4! ]]</EquationSource><EquationSource Format="TEX"><![CDATA[$${v_v} = \sum {_\mu } {R_{v\mu }}{d_\mu }$$

(1)

obtain.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 229.00; Price excludes VAT (USA)

Softcover Book: USD 299.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

References

To be published elsewhere. Cf. also Notes on Lectures on Collision Theory. P. P. Wigner, notes by E. Vogt.
Google Scholar
E. Wigner and L. Eisenbud, Physical Rev. 72, 29 (1947).
Article ADS Google Scholar
Cf. a discussion of a class of functions which include these of J. A. Shohat and J. D. Tatnarkin. The Problem of Moments. Publication of the American Mathematical Society, New York 1943.
Google Scholar
N. G. Van Kampen, Physical Rev. 89, 1072 (1953), 91, 1267 (1953).
Google Scholar
W. Schutzer and J. Tiomno, Physical Rev. 83, 249 (1951).
Article MathSciNet ADS Google Scholar
K. Loewner, Ueber monotone Matrix funktionen. Math. Zeits. 38, 177 (1933).
Google Scholar
J. L. W. V. Jensen, Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Mathematica, 30, 175 (1906).
Article MathSciNet MATH Google Scholar
E. P. Wigner, Amer. Math. Monthly, 59, 669 (1952)
Article MathSciNet MATH Google Scholar
Cf. e.g. H. S. Wall, Analytic Theory of Continued Fractions (Vau Nostrand 1948), p. 15. The notation of this book will be used as far as possible.
Google Scholar
Cf. O. Perron, Die Lehre von den Kettenbruchen, Teuhner 1913, page 264 if.
Google Scholar

Download references

Author information

Authors and Affiliations

The Institute for Advanced Study, Princeton University, USA
E. P. Wigner & J. von Neumann

Authors

E. P. Wigner
View author publications
You can also search for this author in PubMed Google Scholar
J. von Neumann
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

Department of Physics, Joseph Henry Laboratories, Princeton University, Jadwin Hall, 08544, Princeton, NJ, USA
Arthur S. Wightman

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Wigner, E.P., von Neumann, J. (1993). Significance of Loewner’s Theorem in the Quantum Theory of Collisions. In: Wightman, A.S. (eds) The Collected Works of Eugene Paul Wigner. The Collected Works of Eugene Paul Wigner, vol A / 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02781-3_34

Download citation

DOI: https://doi.org/10.1007/978-3-662-02781-3_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08154-5
Online ISBN: 978-3-662-02781-3
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics