Is there an intuitive way of understanding these terms? I understand the mathematics that shows why there are 3 states with proton spins aligned(orthohydrogen) and 1 with spins misaligned. However, when you count them, there are really only 2 states in which the spins are aligned (up-up and down-down). The third one arises from purely mathematical considerations. The same goes for the state when the spins are misaligned (up-down, down-up). What is a better way of thinking about this?