How to get relation for multipole radiation?

In summary, the conversation involved someone reading a quantum mechanics book and needing help deriving a formula for multipole radiation. They were assisted in deriving the formula using the commutator [x, px] = ih and the Hamiltonian H0 = (1/2m) (px2 + py2) + V(r). The formula for multipole radiation is then derived from [xy, H0] = (ih/m)(pxy + xpy). This information was helpful for an upcoming quantum physics exam on Monday.
  • #1
baranas
14
0
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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  • #2
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.
 
  • #3
Thank you, it was very helpful :) at Monday i am having quantum physics exam :rolleyes:
 

Related to How to get relation for multipole radiation?

What is multipole radiation?

Multipole radiation is a type of electromagnetic radiation that is produced by accelerating electric charges and changing electric or magnetic fields. It is characterized by its multipole moments, which describe the distribution of electric charges or currents.

How is multipole radiation related to electromagnetism?

Multipole radiation is a consequence of Maxwell's equations, which describe the behavior of electric and magnetic fields. It is a fundamental aspect of electromagnetism and plays a key role in various phenomena, such as radio waves, light, and X-rays.

What are the different types of multipole radiation?

There are three main types of multipole radiation: dipole radiation, quadrupole radiation, and higher-order multipole radiation. These types are distinguished by the number of poles in the radiation pattern, with dipole radiation having two poles, quadrupole radiation having four poles, and higher-order multipole radiation having more than four poles.

How can I calculate the multipole moments of a radiation source?

The multipole moments of a radiation source can be calculated using mathematical formulas that depend on the geometry and distribution of the source's electric charges or currents. These formulas are derived from Maxwell's equations and can be found in textbooks or online resources.

What are some real-life applications of multipole radiation?

Multipole radiation has many practical applications in our daily lives. For example, dipole radiation is used in radio and television broadcasting, while higher-order multipole radiation is used in medical imaging techniques such as MRI. It is also essential in technologies like wireless communication, satellite communication, and radar systems.

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