Gfrktyl

Whenever I execute the code, portions of the output are null. How can I fix this? I am not sure the extent to which the result is invalid because I am not entirely familiar with the null output, though I have read the documentation. The point in which this problem arises is labeled in the following code:

 omega[t_, t0_, T_] = Exp[(-(t - t0)^2)/T^2];

    omegap[t_, t0p_, Tp_] = Exp[-((t - t0p)^2)/Tp^2];

    eff[t_, t0p_, 

       Tp_] = ((omega[t, t0, T])^2 - (omegap[t, t0p, 

           Tp])^2)/(2 [CapitalDelta]);

    eff[t_, t0p_, 

       Tp_] = (omegap[t, t0p, Tp]*omega[t, t0, T])/([CapitalDelta]);

    ReducedHam = ({

        {[CapitalDelta]eff[t, t0p, Tp], [CapitalOmega]eff[t, t0p, Tp]*

          Exp[Sqrt[-1]*[CurlyPhi]]},

        {[CapitalOmega]eff[t, t0p, Tp]*

          Exp[-Sqrt[-1]*[CurlyPhi]], -[CapitalDelta]eff[t, t0p, Tp]}

       });

    Print[MatrixForm[ReducedHam]]

    [Theta][t_, t0p_, Tp_] = ArcTan[omegap[t, t0p, Tp]/omega[t, t0, T]];

    [Lambda]1 = ({

        {Cos[[Theta]]},

        {-Sin[[Theta]]*Exp[-Sqrt[-1]*[CurlyPhi]]}

       });

    [Lambda]2 = ({

        {Sin[[Theta]]*Exp[Sqrt[-1]*[CurlyPhi]]},

        {Cos[[Theta]]}

       });

    Print[MatrixForm[[Lambda]1]]

    Print[MatrixForm[[Lambda]2]]

    Mat1 = (D[[Lambda]1, [Theta]]).(Transpose[[Lambda]1]);

    Print[Mat1]

    V1 = Transpose[[Lambda]1].D[[Lambda]1, [Theta]];

    V2 = [Lambda]1.Transpose[[Lambda]1];

    Print[MatrixForm[V2]]

    Mat2 = V1[[1, 1]] V2;

    Print[Mat2]

    Dimensions[Mat2];

    Mat12 = Mat1 - Mat2;

    Print[MatrixForm[Mat12]]

    Mat3 = Print[

       MatrixForm[D[[Lambda]2, [Theta]].Transpose[[Lambda]2]]];

    V3 = Transpose[[Lambda]2].D[[Lambda]2, [Theta]];

    V4 = [Lambda]2.Transpose[[Lambda]2];

    Print[MatrixForm[V4]]

    Mat4 = V3[[1, 1]] V4;

    Print[MatrixForm[Mat4]]

    Mat34 = Mat3 - Mat4;

    CDTerm = Mat12 + Mat34 ;

    Print[MatrixForm[Simplify[CDTerm]]]

    (*this is where null arises*)

    TotalHam = ReducedHam + CDTerm;

    Print[MatrixForm[Simplify[TotalHam]]]

    Dimensions[ReducedHam]

    Dimensions[CDTerm]

    [CapitalOmega]a[t_, t0p_, 

      Tp_] = (2 (((D[omega[t, t0, T], t])*(omegap[t, t0p, Tp])) - ((omega[

              t, t0, T]) (D[omegap[t, t0, T], t]))))/((omegap[t, t0, 

          T])^2 + (omega[t, t0, T]^2))

    [Gamma][t_, t0_, T_, [CurlyPhi]_] = 

      ArcTan[([CapitalOmega]a[t, t0p, Tp])/([CapitalOmega]eff[t, t0p, 

           Tp])] + [CurlyPhi];

    f1[t_, t0_, 

      T_, [CurlyPhi]_] = (Exp[(Sqrt[-1]*[Gamma][t, t0, 

           T, [CurlyPhi]])]/2)

    f2[t_, t0_, T_, [CurlyPhi]_] = 

     Exp[(Sqrt[-1]*[Gamma][t, t0, T, [CurlyPhi]])/2]

    U = ({

       {f1[t, t0, T, [CurlyPhi]], 0},

       {0, f2[t, t0, T, [CurlyPhi]]}

      })

    Mat5 = ConjugateTranspose[U].TotalHam.U;

    Print[MatrixForm[Mat5]]

    Mat6 = ConjugateTranspose[U].(D[U, t]);

    Print[MatrixForm[Mat6]]

    HModified = Mat5 - Mat6;

    Print[MatrixForm[Simplify[HModified]]]

Just leave out the Print functions, and remember not to throw away the results with ;. Example:

m1 = IdentityMatrix[3];

MatrixForm[m1]

m2 = 3 m1;

MatrixForm[m2]

Most experienced Mathematica users rarely use Print. To show results, just evaluate them.

A more compact, functional form is:

MatrixForm[m1 = IdentityMatrix[3]]

MatrixForm[m2 = 3 m1]

Same output as above.