Context Navigation

scratchpad4

-              v3
+              v4
 We can also write the equation as
 $\beta = \alpha_0 T'_0 + \displaystyle \sum_{\pm i} \alpha_{\pm i} T'_{\pm \hat{i}} + \sum_{\pm i, \pm j,|i| \ne |j|} \alpha_{\pm i, \pm j} T'_{\pm \hat{i} \pm \hat{j}}$
+$\beta = \alpha_0 T'_0 + \displaystyle \sum_{\pm j} \alpha_{\pm j} T'_{\pm \hat{j}} + \sum_{\pm i, \pm j,|i| \ne |j|} \alpha_{\pm i, \pm j} T'_{\pm \hat{i} \pm \hat{j}}$
 and then work out the coefficients for the matrix equation
 $\alpha_0 = -A -2E_{ii}T_0^\lambda = n \kappa_\parallel \psi$
+$\alpha_0 = -A -2E_{jj}T_0^\lambda = n \kappa_\parallel \psi$
 $\alpha_{\pm i} = \pm C_iT^\lambda_{\pm hat{i}} + E_{ii}T_{\pm \hat{i}}^\lambda$
+$\alpha_{\pm j} = \pm C_jT^\lambda_{\pm \hat{j}} + E_{jj}T_{\pm \hat{j}}^\lambda$