"Laplace transform example 2" a = -(Haa + Hbb + i omega0) b = Haa Hbb - Hab Hba + i Hbb omega0 k = sqrt(4 b - a^2) cb = 2 Hba / k sin(1/2 k t) exp(-1/2 a t) ca = (d(cb,t) - Hbb cb) / (Hba exp(i omega0 t)) check(ca == (cos(1/2 k t) - (a + 2 Hbb) / k sin(1/2 k t)) exp(-i omega0 t) exp(-1/2 a t)) "Verify equation (1)" check(d(ca,t) == Haa ca + Hab cb exp(-i omega0 t)) "ok" "Verify equation (2)" check(d(cb,t) == Hbb cb + Hba ca exp(i omega0 t)) "ok" Haa = 0 Hbb = 0 "Verify equation (6)" check(ca == (cos(1/2 k t) + i omega0 / k sin(1/2 k t)) exp(-1/2 i omega0 t)) "ok" "Verify equation (7)" check(cb == 2 Hba / k sin(1/2 k t) exp(1/2 i omega0 t)) "ok" Run