- #1
M. next
- 382
- 0
We know how to find S[itex]_{x}[/itex] and S[itex]_{y}[/itex] if we used S[itex]_{+}[/itex] and S[itex]_{-}[/itex], and after finding S[itex]_{x}[/itex] and S[itex]_{y}[/itex], we can prove that
[S[itex]_{x}[/itex], S[itex]_{y}[/itex]]= i[itex]\hbar[/itex]S[itex]_{z}[/itex] (Equation 1)
and
[S[itex]_{y}[/itex], S[itex]_{z}[/itex]]= i[itex]\hbar[/itex]S[itex]_{x}[/itex] (Equation 2)
and
[S[itex]_{z}[/itex], S[itex]_{x}[/itex]]= i[itex]\hbar[/itex]S[itex]_{y}[/itex] (Equation 3)
but can we, starting from Equations 1, 2, and 3 find Sx and Sy? Can we work in the opposite direction?
[S[itex]_{x}[/itex], S[itex]_{y}[/itex]]= i[itex]\hbar[/itex]S[itex]_{z}[/itex] (Equation 1)
and
[S[itex]_{y}[/itex], S[itex]_{z}[/itex]]= i[itex]\hbar[/itex]S[itex]_{x}[/itex] (Equation 2)
and
[S[itex]_{z}[/itex], S[itex]_{x}[/itex]]= i[itex]\hbar[/itex]S[itex]_{y}[/itex] (Equation 3)
but can we, starting from Equations 1, 2, and 3 find Sx and Sy? Can we work in the opposite direction?