The “Radial Kinetic Energy” Term in the Schrödinger Equation for a Central Force
作者:
Frank S. Crawford,
期刊:
American Journal of Physics
(AIP Available online 1964)
卷期:
Volume 32,
issue 8
页码: 611-614
ISSN:0002-9505
年代: 1964
DOI:10.1119/1.1970875
出版商: American Association of Physics Teachers
数据来源: AIP
摘要:
A straightforward derivation is given for the Hermitian operatorpr ≡ 1r ħi δδrrcorresponding to the radial component of linear momentum in the central force problem. The purpose is purely pedagogical; we believe that the radial term of the Schrödinger equation in spherical coordinates is more comprehensible when it appears in the form(pr2/2m)ψ = [(1r ħi δδrr)2/2m]ψthan when it appears, as it does in most textbooks, in the form−ħ22mr2 δδr[r2δδr]ψ. The latter expression is usually arrived at by a tedious transformation of variable done “in the appendix”; instead one may deriveprwith a minimum of algebra and with the focus where it belongs, on the concepts of quantum mechanics.
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