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Участник:FeelUs/изоспин
Материал из
https://ru.wikipedia.org
p
=
(
1
0
)
;
{\displaystyle \psi _{p}={\begin{pmatrix}1\\0\end{pmatrix}};}
n
=
(
0
1
)
;
{\displaystyle \psi _{n}={\begin{pmatrix}0\\1\end{pmatrix}};}
=
(
0
1
1
0
)
;
{\displaystyle \tau _{\mu }={\begin{pmatrix}0&1\\1&0\end{pmatrix}};}
=
(
0
i
i
0
)
;
{\displaystyle \tau _{\nu }={\begin{pmatrix}0&-i\\i&0\end{pmatrix}};}
=
(
1
0
0
1
)
=
0
;
{\displaystyle \tau _{\tau }={\begin{pmatrix}1&0\\0&-1\end{pmatrix}}=\tau _{0};}
+
=
(
+
i
)
2
=
1
2
(
0
1
+
i
1
i
0
)
;
{\displaystyle \tau _{+}={\frac {-(\tau _{\mu }+i\tau _{\nu })}{\sqrt {2}}}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}0&-1+i\\-1-i&0\end{pmatrix}};}
+
=
+
2
=
1
2
(
0
1
i
1
+
i
0
)
;
{\displaystyle \tau ^{+}=-{\frac {\tau _{+}}{\sqrt {2}}}={\frac {1}{2}}{\begin{pmatrix}0&1-i\\1+i&0\end{pmatrix}};}
=
+
(
i
)
2
=
1
2
(
0
1
+
i
1
i
0
)
;
{\displaystyle \tau _{-}={\frac {+(\tau _{\mu }-i\tau _{\nu })}{\sqrt {2}}}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}0&1+i\\1-i&0\end{pmatrix}};}
=
2
=
1
2
(
0
1
+
i
1
i
0
)
;
{\displaystyle \tau ^{-}={\frac {\tau _{-}}{\sqrt {2}}}={\frac {1}{2}}{\begin{pmatrix}0&1+i\\1-i&0\end{pmatrix}};}
и должно быть
p
=
n
{\displaystyle \tau ^{-}\psi _{p}=\psi _{n}}
n
=
0
{\displaystyle \tau ^{-}\psi _{n}=0}
+
p
=
0
{\displaystyle \tau ^{+}\psi _{p}=0}
+
n
=
p
{\displaystyle \tau ^{+}\psi _{n}=\psi _{p}}