"WKB method part 2" C = (beta + i k) F exp(i k L - beta L) / (2 beta) D = (beta - i k) F exp(i k L + beta L) / (2 beta) "Verify equation (3)" check(C exp(beta L) + D exp(-beta L) == F exp(i k L)) "ok" "Verify equation (4)" check(beta C exp(beta L) - beta D exp(-beta L) == i k F exp(i k L)) "ok" "Verify equation (7)" A = beta (C - D) / (2 i k) + (C + D) / 2 gamma = (beta / k - k / beta) / 2 check(A == F exp(i k L) (expcosh(beta L) + i gamma expsinh(beta L))) "ok" "Verify equation (8)" M = 1 / (exp(i k L) (expcosh(beta L) + i gamma expsinh(beta L))) T = 1 / (cosh(beta L)^2 + gamma^2 sinh(beta L)^2) check(conj(M) M == T) "ok" "Verify equation (9)" k = sqrt(2 m E / hbar^2) beta = sqrt(2 m (V0 - E) / hbar^2) check(T == (1 + V0^2 / (4 E (V0 - E)) sinh(beta L)^2)^(-1)) "ok" Run