If we imagine a Hamiltonian, H^(r1,r2), describing two identical particles at positions r1 and r2 and then we interchange the particles, the Hamiltonian will be unaffected, i.e. H^(r1,r2)=H^(r2,r1). If we introduce an exchange operator P^r1,r2 such that P^r1,r2H^(r1,r2)=H^(r2,r1)P^r1,r2=H^(r1,r2)P^r1,r2, we see that they commute, or [P^r1,r2,H^(r1,r2)]=0. We know then that P^r1,r2andH^(r1,r2) have common eigenfunctions. We can then easily show that the eigenfunctions of the exchange operator must be either even or odd. Experiments show that odd exchange symmetry corresponds to half-integer spin particles called fermions, while even exchange symmetry corresponds to integer spin particles called bosons. The notes then discuss the implications of the new postulate and then presents the Heitler–London theory and the Heisenberg exchange Hamiltonian which has been so successful in predicting molecular structure.