How to get relation for multipole radiation?

[baranas]

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 :)

 

[Bill_K]

Start with [x, p_x] = ih. From this you can derive [x, p_x²] = x p_x² - p_x² x = (x p_x - p_x x) p_x - p_x(p_xx - xp_x) = 2ih p_x.

Then if H₀ = (1/2m) (p_x² + p_y²) + V(r),

[xy, H₀] = (1/2m)([x, p_x²] y + x [y, p_y²]) = (1/2m)(2ih p_xy + x 2ihp_y) = (ih/m)(p_xy + x p_y)

from which your result follows.

 

[baranas]

Thank you, it was very helpful :) at Monday i am having quantum physics exam