"Verify equation (3)" psi = A(x) exp(i phi(x)) T1 = d(A(x),x,x) T2 = 2 i d(A(x),x) d(phi(x),x) T3 = i A(x) d(phi(x),x,x) T4 = -A(x) d(phi(x),x)^2 check(d(psi,x,x) == (T1 + T2 + T3 + T4) exp(i phi(x))) "ok" "Verify equation (12)" T = 2 m / hbar^2 abs(E - V) T1 = (+sqrt(+T))^(-1/2) T2 = (+sqrt(-T))^(-1/2) T3 = (-sqrt(+T))^(-1/2) T4 = (-sqrt(-T))^(-1/2) check(polar(T1) == T^(-1/4)) check(polar(T2) == exp(-1/4 i pi) T^(-1/4)) check(polar(T3) == exp(-1/2 i pi) T^(-1/4)) check(polar(T4) == exp(-3/4 i pi) T^(-1/4)) "ok" Run