A general expression for the multipole moments of the quantum harmonic oscillator
作者:
Victor Namias,
期刊:
American Journal of Physics
(AIP Available online 1987)
卷期:
Volume 55,
issue 11
页码: 1008-1009
ISSN:0002-9505
年代: 1987
DOI:10.1119/1.14924
出版商: American Association of Physics Teachers
关键词: RECURSION RELATIONS;MULTIPOLES;QUANTUM MECHANICS;HARMONIC OSCILLATORS;WAVE FUNCTIONS;SCHROEDINGER EQUATION
数据来源: AIP
摘要:
Multipole moments for the harmonic oscillator as well as for other familiar quantum systems can be obtained without knowledge of the wavefunction by means of simple recursion relations. The third‐order differential equation satisfied by the probability density is first obtained and from it, the recursion relation for the moments is directly deduced. A general and presumably novel formula giving all the multipole moments is obtained by solving the finite difference equation generated by the recursion relation.
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