in 2 particles system, the Hamiltonian is formed by 2 Hilbert spaces, such that:

for example:

however, it can also be expressed in center of mass – Hilbert space and relative -Hilbert space:

since this is just another factorization, the 2 spaces are still independence. In practice, we have to define position vector for center of mass and relative position:

the corresponding momentum are:

with relations:

thus, the example Hamiltonian becomes:

since the total momentum is just a translation motion of the system, we can safely omit it in most cases and this reduced the 2 body system into 1 body system with fixed center.

### Like this:

Like Loading...

Sharika Abusufait

Apr 21, 2011@ 15:46:21Hi there, I found your blog via Google while searching something and your post looks very spicy for me. Great page you are running there. And many thanks for posting this.

Ricky Ferdolage

Apr 21, 2011@ 17:29:47exquisite work you have done, this site is for real cool with superb info. I suggest you put this article to reddit, and then more and more population might entry your posts. Thank You