原问题是这样的:H 是一个三对角矩阵,有变量k, 我想求其前两个本征值在k=π 的位置的差 y 请问大神该怎么办?
H = {{e[k - 4 π], U0*Sqrt[π/2], 0, 0, 0},
{U0*Sqrt[π/2], e[k - 2 π], U0*Sqrt[π/2], 0, 0},
{0, U0*Sqrt[π/2], e[k], U0*Sqrt[π/2], 0},
{0, 0, U0*Sqrt[π/2], e[k + 2 π], U0*Sqrt[π/2]},
{0, 0, 0, U0*Sqrt[π/2], e[k + 4 π]}};
e[k_] = (k/π)^2;
U0 = 0.5;
e1 = Eigenvalues[H][[1]];
e2 = Eigenvalues[H][[2]];
y=e2-e1
H = {{e[k - 4 π], U0*Sqrt[π/2], 0, 0, 0},
{U0*Sqrt[π/2], e[k - 2 π], U0*Sqrt[π/2], 0, 0},
{0, U0*Sqrt[π/2], e[k], U0*Sqrt[π/2], 0},
{0, 0, U0*Sqrt[π/2], e[k + 2 π], U0*Sqrt[π/2]},
{0, 0, 0, U0*Sqrt[π/2], e[k + 4 π]}};
e[k_] = (k/π)^2;
U0 = 0.5;
e1 = Eigenvalues[H][[1]];
e2 = Eigenvalues[H][[2]];
y=e2-e1