-- Feynman and Hibbs problem 3-12 -- Determine coefficients A, B, and C W = i m omega / (2 hbar sin(omega T)) * ((x^2 + xc^2) cos(omega T) - 2 x xc) - m omega / (2 hbar) (xc - a)^2 C = eval(W, xc, 0) B = eval(W - C, xc^2, 0) A = W - B - C A = eval(A, xc, 1) B = eval(B, xc, 1) "Verify coefficient A" check(A == i m omega exp(i omega T) / (2 hbar sin(omega T))) "ok" "Verify coefficient B" check(B == m omega / hbar (a - i x / sin(omega T))) "ok" "Verify coefficient C" check(C == m omega / (2 hbar) (i x^2 cos(omega T) / sin(omega T) - a^2)) "ok" "Verify equation (6)" check(-pi / A == 2 pi i hbar sin(omega T) / (m omega exp(i omega T))) "ok" "Verify equation (7)" check(-B^2 / (4 A) + C == -m omega / (2 hbar) * (x^2 - 2 a x exp(-i omega T) + a^2 cos(omega T) exp(-i omega T))) "ok" "Verify equation (8)" check(m omega / (2 pi i hbar sin(omega T)) (-pi / A) == exp(-i omega T)) "ok" Run