"Matrix mechanics 3" 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)) PP(f) = P1(P1(f)) + P2(P2(f)) + P3(P3(f)) LL(f) = L1(L1(f)) + L2(L2(f)) + L3(L3(f)) PXL1(f) = P2(L3(f)) - P3(L2(f)) PXL2(f) = P3(L1(f)) - P1(L3(f)) PXL3(f) = P1(L2(f)) - P2(L1(f)) LXP1(f) = L2(P3(f)) - L3(P2(f)) LXP2(f) = L3(P1(f)) - L1(P3(f)) LXP3(f) = L1(P2(f)) - L2(P1(f)) R1(f) = -Z e^2 X1(f) / r + 1 / (2 m) (PXL1(f) - LXP1(f)) R2(f) = -Z e^2 X2(f) / r + 1 / (2 m) (PXL2(f) - LXP2(f)) R3(f) = -Z e^2 X3(f) / r + 1 / (2 m) (PXL3(f) - LXP3(f)) RR(f) = R1(R1(f)) + R2(R2(f)) + R3(R3(f)) H(f) = PP(f) / (2 m) - Z e^2 / r f r = sqrt(x1^2 + x2^2 + x3^2) Y = psi(x1,x2,x3,t) "Verify equation (4.8.7) for wavefunctions" check(RR(Y) == Z^2 e^4 Y + 2 / m H(LL(Y) + hbar^2 Y)) "ok" "Verify commutation relations" check(R1(H(Y)) == H(R1(Y))) check(R2(H(Y)) == H(R2(Y))) check(R3(H(Y)) == H(R3(Y))) check(RR(H(Y)) == H(RR(Y))) "ok" Run