ABSTRACT
Consider a pair of particles that may be either two fermions or two bosons. e Schrödinger equation for the system is written in terms of the Hamiltonian operator for the system as
H( , ) ( , ) ( , ),1 2 1 2 1 2c c= E (12.1)
where 1 represents the coordinates of particle 1 and 2 the coordinates of particle 2. e Hamiltonian (1, 2) must be symmetric under particle interchange because of the indistinguishability of the particles, giving
H H( , ) ( , ).1 2 2 1= (12.2)
e pair wave function χ(1, 2) may be either symmetric or antisymmetric. is can be seen by introducing the permutation operator P12, which permutes the coordinates of the particles.
