Algebraic calculation of nonrelativistic coulomb phase shifts

Daniel Zwanziger

doi:10.1063/1.1705429

Algebraic calculation of nonrelativistic coulomb phase shifts

Daniel Zwanziger

Research output: Contribution to journal › Article › peer-review

Abstract

It is observed that the in and out states of a particle of energy k ²/2m, entering or leaving a Coulomb field along the +z direction, are eigenstates of L₃ with eigenvalue 0, and of A₃, the third component of the Runge-Lenz vector, with eigenvalues ±αx+ik/m, respectively. From this characterization and the commutation relations of the symmetry group, the phase shifts are easily obtained algebraically.

Original language	English (US)
Pages (from-to)	1858-1860
Number of pages	3
Journal	Journal of Mathematical Physics
Volume	8
Issue number	9
DOIs	https://doi.org/10.1063/1.1705429
State	Published - 1967

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.1705429

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title = "Algebraic calculation of nonrelativistic coulomb phase shifts",

abstract = "It is observed that the in and out states of a particle of energy k 2/2m, entering or leaving a Coulomb field along the +z direction, are eigenstates of L3 with eigenvalue 0, and of A3, the third component of the Runge-Lenz vector, with eigenvalues ±αx+ik/m, respectively. From this characterization and the commutation relations of the symmetry group, the phase shifts are easily obtained algebraically.",

author = "Daniel Zwanziger",

year = "1967",

doi = "10.1063/1.1705429",

language = "English (US)",

volume = "8",

pages = "1858--1860",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

publisher = "American Institute of Physics",

number = "9",

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T1 - Algebraic calculation of nonrelativistic coulomb phase shifts

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PY - 1967

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N2 - It is observed that the in and out states of a particle of energy k 2/2m, entering or leaving a Coulomb field along the +z direction, are eigenstates of L3 with eigenvalue 0, and of A3, the third component of the Runge-Lenz vector, with eigenvalues ±αx+ik/m, respectively. From this characterization and the commutation relations of the symmetry group, the phase shifts are easily obtained algebraically.

AB - It is observed that the in and out states of a particle of energy k 2/2m, entering or leaving a Coulomb field along the +z direction, are eigenstates of L3 with eigenvalue 0, and of A3, the third component of the Runge-Lenz vector, with eigenvalues ±αx+ik/m, respectively. From this characterization and the commutation relations of the symmetry group, the phase shifts are easily obtained algebraically.

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DO - 10.1063/1.1705429

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JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 9

ER -

Algebraic calculation of nonrelativistic coulomb phase shifts

Abstract

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