How to get relation for multipole radiation?

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SUMMARY

The discussion focuses on deriving the relation formula for multipole radiation using principles from quantum mechanics, specifically referencing Davydov A.S.'s textbook. The derivation begins with the commutation relation [x, px] = ih and progresses to [x, px2] = 2ih px. The Hamiltonian is defined as H0 = (1/2m)(px2 + py2) + V(r), leading to the result [xy, H0] = (ih/m)(pxy + x py), which is essential for understanding multipole radiation in quantum physics.

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baranas
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At the moment i am reading Davydov A.S. Quantum mechanics book. And i need help to derive relation formula for multipole radiation
[PLAIN]http://img827.imageshack.us/img827/8974/formulal.png
Thank you in advance :)
 

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Start with [x, px] = ih. From this you can derive [x, px2] = x px2 - px2 x = (x px - px x) px - px(pxx - xpx) = 2ih px.

Then if H0 = (1/2m) (px2 + py2) + V(r),

[xy, H0] = (1/2m)([x, px2] y + x [y, py2]) = (1/2m)(2ih pxy + x 2ihpy) = (ih/m)(pxy + x py)

from which your result follows.
 
Thank you, it was very helpful :) at Monday i am having quantum physics exam :rolleyes:
 

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