Para / Ortho Hydrogen (H2) Spins

[YAHA]

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?

 

[zincshow]

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?

This picture provides an intuitive way of visually representing the different types of spin. Think of the para form as having the spin of the two protons "locked" together. The ortho form allows the two protons to be "locked" together 3 different ways, both up, one up/one down, both down.

 

[DrDu]

Maybe it helps to remind yourself that a state like $1/\sqrt{2}(|\uparrow\rangle \pm |\downarrow \rangle)$ for a single spin is an eigenstate with the spin pointing in plus or minus the x direction. You can show that the two particle state with m=0 actually is a superposition of both spins pointing in the same direction in the x or y directions.