【正文】 Normal[Series[Simplify[Ulh=Transpose[U34].,AssumptionsElement[k,Reals]],{k,0,2}]]//FullSimplify{{0,0,0,0,0},{0,0,0,0,0},{0,0,k^2 u3^2,0,0},{0,0,0,1+k^2 u3 Conjugate[u3],0},{0,0,0,0,0}}MatrixForm[%](0 0 0 0 00 0 0 0 00 0 k^2 u3^2 0 00 0 0 1+k^2 u3 Conjugate[u3] 00 0 0 0 0)Normal[Simplify[Ulh=Transpose[U34].,AssumptionsElement[k,Reals]]]//FullSimplify{{0,0,0,0,0},{0,0,0,0,0},{0,0,k^2 u3^2 (1+k^2 u3 Conjugate[u3]),1/4 k^3 u3 Abs[u3]^2 (6+k^2 u3 Conjugate[u3]),0},{0,0,1/4 k^3 u3 Abs[u3]^2 (6+k^2 u3 Conjugate[u3]),13/4 k^4 Abs[u3]^4+k^2 u3 Conjugate[u3],0},{0,0,0,0,0}}MatrixForm[%](0 0 0 0 00 0 0 0 00 0 k^2 u3^2 (1+k^2 u3 Conjugate[u3]) 1/4 k^3 u3 Abs[u3]^2 (6+k^2 u3 Conjugate[u3]) 00 0 1/4 k^3 u3 Abs[u3]^2 (6+k^2 u3 Conj。Normal[Series[Simplify[Ulh=Transpose[U24].,AssumptionsElement[k,Reals]],{k,0,2}]]//FullSimplify{{0,0,0,0,0},{0,k^2 u2^2,0,0,0},{0,0,0,0,0},{0,0,0,1+k^2 u2 Conjugate[u2],0},{0,0,0,0,0}}MatrixForm[%](0 0 0 0 00 k^2 u2^2 0 0 00 0 0 0 00 0 0 1+k^2 u2 Conjugate[u2] 00 0 0 0 0)Normal[Simplify[Ulh=Transpose[U24].,AssumptionsElement[k,Reals]]]//FullSimplify{{0,0,0,0,0},{0,k^2 u2^2 (1+k^2 u2 Conjugate[u2]),0,1/4 k^3 u2 Abs[u2]^2 (6+k^2 u2 Conjugate[u2]),0},{0,0,0,0,0},{0,1/4 k^3 u2 Abs[u2]^2 (6+k^2 u2 Conjugate[u2]),0,13/4 k^4 Abs[u2]^4+k^2 u2 Conjugate[u2],0},{0,0,0,0,0}}MatrixForm[%](0 0 0 0 00 k^2 u2^2 (1+k^2 u2 Conjugate[u2]) 0 1/4 k^3 u2 Abs[u2]^2 (6+k^2 u2 Conjugate[u2]) 00 0 0 0 00 1/4 k^3 u2 Abs[u2]^2 (6+k^2 u2 Conjugate[u2]) 0 13/4 k^4 Abs[u2]^4+k^2 u2 Conjugate[u2] 00 0 0 0 0)M34=(0 0 0 0 00 0 0 0 00 0 0 ku3 00 0 ku3 1 00 0 0 0 0)。Normal[Series[Simplify[Ulh=Transpose[U14].,AssumptionsElement[k,Reals]],{k,0,2}]]//FullSimplify{{k^2 u1^2,0,0,0,0},{0,0,0,0,0},{0,0,0,0,0},{0,0,0,1+k^2 u1 Conjugate[u1],0},{0,0,0,0,0}}MatrixForm[%](k^2 u1^2 0 0 0 00 0 0 0 00 0 0 0 00 0 0 1+k^2 u1 Conjugate[u1] 00 0 0 0 0)Normal[Simplify[Ulh=Transpose[U14].,AssumptionsElement[k,Reals]]]//FullSimplify{{k^2 u1^2 (1+k^2 u1 Conjugate[u1]),0,0,1/4 k^3 u1 Abs[u1]^2 (6+k^2 u1 Conjugate[u1]),0},{0,0,0,0,0},{0,0,0,0,0},{1/4 k^3 u1 Abs[u1]^2 (6+k^2 u1 Conjugate[u1]),0,0,13/4 k^4 Abs[u1]^4+k^2 u1 Conjugate[u1],0},{0,0,0,0,0}}MatrixForm[%](k^2 u1^2 (1+k^2 u1 Conjugate[u1]) 0 0 1/4 k^3 u1 Abs[u1]^2 (6+k^2 u1 Conjugate[u1]) 00 0 0 0 00 0 0 0 01/4 k^3 u1 Abs[u1]^2 (6+k^2 u1 Conjugate[u1]) 0 0 13/4 k^4 Abs[u1]^4+k^2 u1 Conjugate[u1] 00 0 0 0 0)M24=(0 0 0 0 00 0 0 ku2 00 0 0 0 00 ku2 0 1 00 0 0 0 0)。M14=(0 0 0 ku1 00 0 0 0 00 0 0 0 0ku1 0 0 1 00 0 0 0 0)。kv2=k Abs[v2] Exp[I Arg[v2]]。ku3=k Abs[u3] Exp[I Arg[u3]]。Normal[Series[Simplify[Ulh=,AssumptionsElement[k,Reals]],{k,0,2}]]//FullSimplify{{11/2 k^2 u1 Conjugate[u1],k^2 u2 Conjugate[u1],k^2 u3 Conjugate[u1],k Conjugate[u1]},{0,11/2 k^2 u2 Conjugate[u2],k^2 u3 Conjugate[u2],k Conjugate[u2]},{0,0,11/2 k^2 u3 Conjugate[u3],k Conjugate[u3]},{k u1,k u2,k u3,11/2 k^2 (Abs[u1]^2+Abs[u2]^2+Abs[u3]^2)}}MatrixForm[%](11/2 k^2 u1 Conjugate[u1] k^2 u2 Conjugate[u1] k^2 u3 Conjugate[u1] k Conjugate[u1]0 11/2 k^2 u2 Conjugate[u2] k^2 u3 Conjugate[u2] k Conjugate[u2]0 0 11/2 k^2 u3 Conjugate[u3] k Conjugate[u3]k u1 k u2 k u3 11/2 k^2 (Abs[u1]^2+Abs[u2]^2+Abs[u3]^2))Normal[Series[Simplify[Transpose[Ulh].,AssumptionsElement[k,Reals]],{k,0,2}]]//FullSimplify{{k^2 u1^2,k^2 u1 u2,k^2 u1 u3,0},{k^2 u1 u2,k^2 u2^2,k^2 u2 u3,0},{k^2 u1 u3,k^2 u2 u3,k^2 u3^2,0},{0,0,0,1+k^2 (Abs[u1]^2+Abs[u2]^2+Abs[u3]^2)}}MatrixForm[%](k^2 u1^2 k^2 u1 u2 k^2 u1 u3 0k^2 u1 u2 k^2 u2^2 k^2 u2 u3 0k^2 u1 u3 k^2 u2 u3 k^2 u3^2 00 0 0 1+k^2 (Abs[u1]^2+Abs[u2]^2+Abs[u3]^2))附錄II 五代中微子的計(jì)算程序ku1=k Abs[u1] Exp[I Arg[u1]]。U34=(1 0 0 00 1 0 00 0 1ku3 Conjugate[ku3]/2 Conjugate[ku3]0 0 ku3 1ku3 Conjugate[ku3]/2)。Normal[Series[Simplify[Ulh=Transpose[U34].,AssumptionsElement[k,Reals]],{k,0,2}]]//FullSimplify{{0,0,0,0},{0,0,0,0},{0,0,k^2 u3^2,0},{0,0,0,1+k^2 u3 Conjugate[u3]}}MatrixForm[%](0 0 0 00 0 0 00 0 k^2 u3^2 00 0 0 1+k^2 u3 Conjugate[u3])Normal[Simplify[Ulh=Transpose[U34].,AssumptionsElement[k,Reals]]]//FullSimplify{{0,0,0,0},{0,0,0,0},{0,0,k^2 u3^2 (1+k^2 u3 Conjugate[u3]),1/4 k^3 u3 Abs[u3]^2 (6+k^2 u3 Conjugate[u3])},{0,0,1/4 k^3 u3 Abs[u3]^2 (6+k^2 u3 Conjugate[u3]),13/4 k^4 Abs[u3]^4+k^2 u3 Conjugate[u3]}}MatrixForm[%](0 0 0 00 0 0 00 0 k^2 u3^2 (1+k^2 u3 Conjugate[u3]) 1/4 k^3 u3 Abs[u3]^2 (6+k^2 u3 Conjugate[u3])0 0 1/4 k^3 u3 Abs[u3]^2 (6+k^2 u3 Conjugate[u3]) 13/4 k^4 Abs[u3]^4+k^2 u3 Conjugate[u3])U14=(1ku1 Conjugate[ku1]/2 0 0 Conjugate[ku1]0 1 0 00 0 1 0 ku1 0 0 1ku1 Conjugate[ku1]/2)。Normal[Series[Simplify[Ulh=Transpose[U24].,AssumptionsElement[k,Reals]],{k,0,2}]]//FullSimplify{{0,0,0,0},{0,k^2 u2^2,0,0},{0,0,0,0},{0,0,0,1+k^2 u2 Conjugate[u2]}}MatrixForm[%](0 0 0 00 k^2 u2^2 0 00 0 0 00 0 0 1+k^2 u2 Conjugate[u2])Normal[Simplify[Ulh=Transpose[U24].,AssumptionsElement[k,Reals]]]//FullSimplify{{0,0,0,0},{0,k^2 u2^2 (1+k^2 u2 Conjugate[u2]),0,1/4 k^3 u2 Abs[u2]^2 (6+k^2 u2 Conjugate[u2])},{0,0,0,0},{0,1/4 k^3 u2 Abs[u2]^2 (6+k^2 u2 Conjugate[u2]),0,13/4 k^4 Abs[u2]^4+k^2 u2 Conjugate[u2]}}MatrixForm[%](0 0 0 00 k^2 u2^2 (1+k^2 u2 Conjugate[u2]) 0 1/4 k^3 u2 Abs[u2]^2 (6+k^2 u2 Conjugate[u2])0 0 0 00 1/4 k^3 u2 Abs[u2]^2 (6+k^2 u2 Conjugate[u2]) 0 13/4 k^4 Abs[u2]^4+k^2 u2 Conjugate[u2])M34=(0 0 0 00 0 0 00 0 0 ku30 0 ku3 1)。Normal[Series[Simplify[Ulh=Transpose[U14].,AssumptionsElement[k,Reals]],{k,0,2}]]//FullSimplify{{k^2 u1^2,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,1+k^2 u1 Conjugate[u1]}}MatrixForm[%](k^2 u1^2 0 0 00 0 0 00 0 0 00 0 0 1+k^2 u1 Conjugate[u1])Normal[Simplify[Ulh=Transpose[U14].,AssumptionsElement[k,Reals]]]//FullS