Thanks for your answer.
I found a lot of nice commands but Mathematica don't work. My code is for the equation are
eoMkitaevchaindiracnormal = {
-I c1'[t] == -\[Omega] (c2[t] + ConjugateTranspose[c2[t]]) +
Exp[-((x1 - v*t)^2/(2 \[Sigma]^2))]/
2 c1[t], -I ConjugateTranspose[c1]'[
t] == \[Omega] (c2[t] + ConjugateTranspose[c2[t]]) +
Exp[-((x1 - v*t)^2/(2 \[Sigma]^2))]/
2 ConjugateTranspose[c1[t]], -I c2'[
t] == -\[Omega] (c1[t] - ConjugateTranspose[c1[t]]) +
Exp[-((x2 - v*t)^2/(2 \[Sigma]^2))]/
2 c2[t], -I ConjugateTranspose[c2]'[
t] == \[Omega] (-c1[t] + ConjugateTranspose[c1[t]]) +
Exp[-((x2 - v*t)^2/(2 \[Sigma]^2))]/2 ConjugateTranspose[c2[t]], ,
c1[-100] == 1, c2[-100] == 1, ConjugateTranspose[c1][-100] == 1,
ConjugateTranspose[c2][-100] == 1};
Now, I want use NDSolve to solve the equation and use this code
solutionkitaevchaindiracnormal =
NDSolve[eoMkitaevchaindiracnormal /. {v0 -> 1,
v -> 1, \[Sigma] -> 0.75, x1 -> 1, x2 -> 2, \[Omega] -> 1}, {c1[
t], c2[t], ConjugateTranspose[c1][t],
ConjugateTranspose[c2][t]}, {t, -100, 100}];
After the second step Mathematics give me this Output:
NDSolve::deqn: Equation or list of equations expected instead of Null in the first argument {-I c1^\[Prime](t)==1/2 E^(-0.888889 Plus[<<2>>]^2) c1(t)-c2(t)-c2(t)^\[ConjugateTranspose],-I ((c1^\[ConjugateTranspose])^\[Prime])\[InvisibleApplication](t)==c2(t)+1/2 E^(-0.888889 Plus[<<2>>]^2) c1(t)^\[ConjugateTranspose]+c2(t)^\[ConjugateTranspose],-I c2^\[Prime](t)==-c1(t)+1/2 E^(-0.888889 Plus[<<2>>]^2) c2(t)+c1(t)^\[ConjugateTranspose],-I ((c2^\[ConjugateTranspose])^\[Prime])\[InvisibleApplication](t)==-c1(t)+c1(t)^\[ConjugateTranspose]+1/2 E^(-0.888889 Plus[<<2>>]^2) c2(t)^\[ConjugateTranspose],Null,c1(-100)==1,c2(-100)==1,(c1^\[ConjugateTranspose])\[InvisibleApplication](-100)==1,(c2^\[ConjugateTranspose])\[InvisibleApplication](-100)==1}. >>
What is my mistake?
Can I use ConjugateTranspose too describe a creation operator or I have use an other command ?