deletions | additions       diff --git a/textbf_Absence_of_back_scattering__.tex b/textbf_Absence_of_back_scattering__.tex  index c05f788..d2b036e 100644  --- a/textbf_Absence_of_back_scattering__.tex  +++ b/textbf_Absence_of_back_scattering__.tex 
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\end{equation}  If we apply the $T$ to the state, we have  \begin{equation}  -T\psi=-\sum_{s\in(L,R)}a^{in*}_{s}\psi^{out}_{s}+\sum_{s\in(L,R)}(S^{*}a^{in*}_{s})_{s}\psi^{in}_{s} -T\psi=-\sum_{s\in(L,R)}a^{in*}_{s}\psi^{out}_{s}+\sum_{s\in(L,R)}(S^{*}a^{in*}_{s})_{s}\psi^{in}_{s}\\  =\sum_{s\in(L,R)}(S^{*}a^{in*}_{s})_{s}\psi^{in}_{s}+\sum_{s\in(L,R)}(-S^{T}S^{*}a^{in*}_{s})_{s}\psi^{out}_{s}  \end{equation}  A direct consequence of (18) is that $S=-S^{T}$, which is