Im having trouble with my thought process for spin states of a system of two electrons(adsbygoogle = window.adsbygoogle || []).push({});

Using Total Spin 'S' and Total spin mag quantum numbers 'M_{S}' as state ket |S M_{S}>

My textbook states....

" Three Symmetric Spin states

Triplet spin stats for twin identical spin -1/2 particles

My thought process, two half spin particles are involved so total spin S is 1/2 + 1/2=1 and two spin ups giving M

- | Up Up> = |S M
_{S}> = |1, 1> "_{S}as +1/2 + 1/2 =1

I see this, again two spin particles are involved so its 1 again. However this time M

- " 1/√2 ( |Up Down> + |Down Up> ) = |1,0> "
_{S}we two zeros in the bracket, ( (1/2 - 1/2) + (1/2 - 1/2) ) giving overall zero.

I understand, same reasoning as point 1. Total spin as 1 from two half spin particles, and two -1/2 for M

- " | Up Up> = |S M
_{S}> = |1, -1> "_{S}giving -1.

" One Antisymmetric spin state

Singlet spin state for two identical spin-1/2 particles

By my reasoning for the others, this has two spin particles of 1/2 so total spin should be 1 and M

- 1/√2 ( |Up Down> - |Down Up> ) = |0,0> "
_{S}zero again..... What is wrong with my though process for how the Total spin and total mag quantum numbers are worked... How are totals calculated?

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# I Spin states for two identical 1/2 particles - Confused :s

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