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## Main Question or Discussion Point

I am studying the deuterium's nucleus.

As we know, there are just two eigenstates for a spin 1/2 particle: either spin up or spin down.

Thus, over the whole nucleus, you get 4 possible combinations:

1) Spin up-spin up

2) Spin up-spin down

3) Spin down-spin up

4) Spin down-spin down

If you add the spins up, the four cases, you get +1, 0, 0, -1 respectively.

S = 1 means there are 3 possible values for the total nuclear spin of the nucleus, while s = 0 means there is just 1 possible value.

You can watch the enlightening Dr. Physics video on nuclear spin for further details:

But I have been told there are just two possible cases instead: Spin up-spin up and Spin up-spin down.

I asked why and the following table was used to argue it:

Note that here the cases are not as expected; the eigenstate of the neutron never is spin-down...

As we know, there are just two eigenstates for a spin 1/2 particle: either spin up or spin down.

Thus, over the whole nucleus, you get 4 possible combinations:

1) Spin up-spin up

2) Spin up-spin down

3) Spin down-spin up

4) Spin down-spin down

If you add the spins up, the four cases, you get +1, 0, 0, -1 respectively.

S = 1 means there are 3 possible values for the total nuclear spin of the nucleus, while s = 0 means there is just 1 possible value.

You can watch the enlightening Dr. Physics video on nuclear spin for further details:

But I have been told there are just two possible cases instead: Spin up-spin up and Spin up-spin down.

I asked why and the following table was used to argue it:

Note that here the cases are not as expected; the eigenstate of the neutron never is spin-down...

**May you shed some light on why I am wrong assuming four possible eigenstates for the coupled proton-neutron case and on how to interpret the attached table?**

Note: what I think it is going on here is that the general state of deuterium is just the normalized linear combination of both spin-up and spin-down, but I want to go further than that.

ThanksNote: what I think it is going on here is that the general state of deuterium is just the normalized linear combination of both spin-up and spin-down, but I want to go further than that.

Thanks