- #1
RedX
- 970
- 3
Why is a deuteron an antisymmetric singlet in isospin:
[tex]|\uparrow\downarrow>-|\downarrow\uparrow>=|0,0> [/tex]
whereas a proton and neutron that are separated are a combination of an antisymmetric singlet and a symmetric triplet:
[tex]|\uparrow\downarrow>=|0,0>+|1,0> [/tex]
I don't understand the difference. Isn't a deuteron a neutron and a proton? (the spin up arrow stands for a proton state, and the spin down arrow a neutron state).
I read somewhere that a deuteron is antisymmetric in isospin because it is composed of two identical fermions so that the wavefunction needs to be antisymmetric! Since when was a proton identical to a neutron? And why doesn't that logic hold for a proton and a neutron that are separated?
[tex]|\uparrow\downarrow>-|\downarrow\uparrow>=|0,0> [/tex]
whereas a proton and neutron that are separated are a combination of an antisymmetric singlet and a symmetric triplet:
[tex]|\uparrow\downarrow>=|0,0>+|1,0> [/tex]
I don't understand the difference. Isn't a deuteron a neutron and a proton? (the spin up arrow stands for a proton state, and the spin down arrow a neutron state).
I read somewhere that a deuteron is antisymmetric in isospin because it is composed of two identical fermions so that the wavefunction needs to be antisymmetric! Since when was a proton identical to a neutron? And why doesn't that logic hold for a proton and a neutron that are separated?