Explanation: has to do with the symmetry of identical particles. Take a spin 1/2 particle. It can be up or down, u or d. Suppose we have two such, 1 and 2. Then there are four combinations possible: u1xu2, u1xd2, u2xd1, d1xd2
Explanation: has to do with the symmetry of identical particles. Take a spin 1/2 particle. It can be up or down, u or d. Suppose we have two such, 1 and 2. Then there are four combinations possible: u1xu2, u1xd2, u2xd1, d1xd2
Now suppose that the two particles are identical, in the quantum sense. Then the physical situation can’t change when we interchange the labels. So the square of the wave function can change, because that is physically observable. The sign of the wave function could change, though. The first and last of the four states are symmetrical under interachange of the 1,2 label, but the middle ones have no symmetry: does not have any symmetry