# 3 Non-Identical Particle System

1. Oct 27, 2007

### sn1986j

1. The problem statement, all variables and given/known data
A system of three non-identical spin one-half particles, whose spin operators are (vectors) s1, s2, s3, is governed by the Hamiltonian

H=A s1(dot)s2 + B (s1+s2)(dot)s3

Find the energy levels and their degeneracies.

2. Relevant equations
psi=(phi1)(phi2)(phi3)
Hphi=Ephi

3. The attempt at a solution
As non identical particles, I realize that I have to construct a function where psi=(phi1)(phi2)(phi3) and then apply the hamiltonian <psi(H)psi>=E. My problem is that I am having a hard time dealing with generalized operators. Normally, spin operators are given as hbar/2 time the respective pauli matrix. So in this case, are my spin operators still functions of the pauli matrices? How do I denote different states for each vector and how do I apply the spin operators without them being specified? I am very confused.

Also, I am unsure as to what A and B are - are they specific values/functions? or are they just general constants?

2. Oct 28, 2007

### dextercioby

A and B are general constants. What is the dimension of the space in which the Hamiltonian is a linear operator ?

3. Oct 28, 2007