"Orbital angular momentum 1" 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)) Lsq(f) = L1(L1(f)) + L2(L2(f)) + L3(L3(f)) psi = Psi(x1,x2,x3,t) "Verify equation (1)" 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) "ok" "Verify equation (2)" 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) "ok" "Verify equation (3)" check(L1(Lsq(psi)) - Lsq(L1(psi)) == 0) check(L2(Lsq(psi)) - Lsq(L2(psi)) == 0) check(L3(Lsq(psi)) - Lsq(L3(psi)) == 0) "ok" "Verify equation (4)" check(L2(L3(psi)) - L3(L2(psi)) == i hbar L1(psi)) check(L3(L1(psi)) - L1(L3(psi)) == i hbar L2(psi)) check(L1(L2(psi)) - L2(L1(psi)) == i hbar L3(psi)) "ok" "Verify equation (5)" PxL = (P2(L3(psi)) - P3(L2(psi)), P3(L1(psi)) - P1(L3(psi)), P1(L2(psi)) - P2(L1(psi))) LxP = (L2(P3(psi)) - L3(P2(psi)), L3(P1(psi)) - L1(P3(psi)), L1(P2(psi)) - L2(P1(psi))) P = (P1(psi),P2(psi),P3(psi)) check(PxL + LxP == 2 i hbar P) "ok" "Verify equation (6)" check(1/2 (PxL - LxP) == PxL - i hbar P) "ok" "Verify equation (7)" epsilon = (((0,0,0),(0,0,1),(0,-1,0)), ((0,0,-1),(0,0,0),(1,0,0)), ((0,1,0),(-1,0,0),(0,0,0))) S(I1,I2) = epsilon[I1,I2,1] P1(psi) + epsilon[I1,I2,2] P2(psi) + epsilon[I1,I2,3] P3(psi) check(L1(P1(psi)) - P1(L1(psi)) == i hbar S(1,1)) check(L1(P2(psi)) - P2(L1(psi)) == i hbar S(1,2)) check(L1(P3(psi)) - P3(L1(psi)) == i hbar S(1,3)) check(L2(P1(psi)) - P1(L2(psi)) == i hbar S(2,1)) check(L2(P2(psi)) - P2(L2(psi)) == i hbar S(2,2)) check(L2(P3(psi)) - P3(L2(psi)) == i hbar S(2,3)) check(L3(P1(psi)) - P1(L3(psi)) == i hbar S(3,1)) check(L3(P2(psi)) - P2(L3(psi)) == i hbar S(3,2)) check(L3(P3(psi)) - P3(L3(psi)) == i hbar S(3,3)) "ok" Run