phi = sqrt(2 / a) sin(n pi x / a) E = hbar^2 / (2 m) (n pi / a)^2 psi(t) = phi exp(-i E t / hbar) "Verify wavefunction in (b)" check(-hbar^2 / (2 m) d(psi,x,x) == i hbar d(psi,t)) "ok" G = exp(-i E (t2 - t1) / hbar) "Verify propagator in (b)" check(psi(t2) == G psi(t1)) "ok" "Verify integral in (c)" f = exp(-i En t / hbar) exp(i (omega + i epsilon) t / hbar) I = integral(f,t) G = 0 - eval(I,t,0) check(G == i hbar / (omega - En + i epsilon)) "ok" Run