[題目] 同位旋問題和態的運算
[領域] 近代物理 (題目相關領域)
[來源] 參考書編輯為考古題 (課本習題、考古題、參考書...)
[題目]
Isospin is a symmetry introduced by Heisnberg to explain some properties of
nuclear interactions involving proton(p), neutron(n), and pion(π). Proton
is assigned to have isospin l=1/2 with the z-component l_z=1/2(i.e |1/2,1/2>
or isospin up state)；neutron is assigned to the |1/2,-1/2> state. What will
be the possible isospin state for deuteron? You can copy the idea for the
addition of the angular momentum here to the case of isospin since they
behave the same mathematically. If you know that Δ^+ is assigned to the
isospin |3/2,1/2> state and Δ^+ can decay either to pπ^0 or to nπ^+ ,what
will be the decay percentage for each mode assuming isospin is a good
symmetry? Note that π^+ is an isospin |1,1> state , and π^0 is |1,0> state;
the ladder operator for spin has the following relationship in Natural unit:
S |sm>=√([s(s+1)-m(m+1) ] )|s(m-1)>
[瓶頸] 對態的運算有困難
請各位幫忙
(寫寫自己的想法，方便大家為你解答)
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