The kinetic energy terms in the Hamiltonian are independent.
There may be an interaction between the two particles in the potential.
The **Hamiltonian for two particles** can be easily written.

Often, the potential will only depend on the
**difference in the positions of the two particles**.

This means that the overall

transforms to

which can be Taylor expanded

We can write the derivatives in terms of the total momentum operator.

Subtract of the initial Schrödinger equation and commute through .

We have proven that

if the Hamiltonian has translational symmetry. The

Jim Branson 2013-04-22