"Angular momentum" X1(f) = x1 f X2(f) = x2 f X3(f) = x3 f P1(f) = -i hbar d(f,x1) P2(f) = -i hbar d(f,x2) P3(f) = -i hbar d(f,x3) L1(f) = X2(P3(f)) - X3(P2(f)) L2(f) = X3(P1(f)) - X1(P3(f)) L3(f) = X1(P2(f)) - X2(P1(f)) psi = Psi(x1,x2,x3) check(X1(L3(psi)) - L3(X1(psi)) == -i hbar X2(psi)) check(X2(L3(psi)) - L3(X2(psi)) == i hbar X1(psi)) check(X3(L3(psi)) - L3(X3(psi)) == 0) check(P1(L3(psi)) - L3(P1(psi)) == -i hbar P2(psi)) check(P2(L3(psi)) - L3(P2(psi)) == i hbar P1(psi)) check(P3(L3(psi)) - L3(P3(psi)) == 0) Lsq(f) = L1(L1(f)) + L2(L2(f)) + L3(L3(f)) check(L1(Lsq(psi)) == Lsq(L1(psi))) check(L2(Lsq(psi)) == Lsq(L2(psi))) check(L3(Lsq(psi)) == Lsq(L3(psi))) J1(f) = L1(f) / hbar J2(f) = L2(f) / hbar J3(f) = L3(f) / hbar check(J1(J2(psi)) - J2(J1(psi)) == i J3(psi)) check(J2(J3(psi)) - J3(J2(psi)) == i J1(psi)) check(J3(J1(psi)) - J1(J3(psi)) == i J2(psi)) "ok" Run