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Canadian Journal of Physics

NOTE ON THE RELATION BETWEEN FEYNMAN'S FORMULATION OF SCATTERING PROBLEMS AND THE BORN APPROXIMATION

John Robert Hugh Dempster

Published Jan 1, 1951• 0 citations
Publisher

Abstract

Feynman's formulation of scattering problems is described briefly, and is compared with Born's approximation. The two procedures are shown to be equivalent and to be valid under the same conditions. Feynman's formulas are used to calculate the first and second order terms of the scattered particle wave function, with an arbitrary scattering potential.

DOI
10.1139/p51-007

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Feynman's formulation of scattering problems is described briefly, and is compared with Born's approximation. The two procedures are shown to be equivalent and to be valid under the same conditions. Feynman's formulas are used to calculate the first and second order terms of the scattered particle wave function, with an arbitrary scattering potential.
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The exact solution to the problem of scattering of electrons by a solenoid of infinite length is studied in two limiting cases; firstly, when the radius r 0 to 0 with the enclosed flux phi held constant, and secondly, when phi to 0 with r 0 held constant. Previously reported discrepancies between the Born approximation and the Aharonov-Bohm solution of this problem are reconciled and conditions for the validity of each of these two approximations are established. The relevance of the results to a related scattering problem involving crystal dislocations is briefly discussed and in this case the Born approximation is shown to be valid over almost all the Fermi surface.