What is the commutation relationship between the total angular momentum operator L2 and any of its components, e.g., Lx​?OPTIONS [L2,Lx​]= -iℏLx [L2,Lx​]=0 [L2,Lx​]= iℏLx [L2,Lx​]= ℏ

Which of the following commutation relations holds for the angular momentum operators in quantum mechanics?OPTIONS [Lx, Ly] = iħLz [Lx, Ly] = 0 [Lx, Ly] = -iħLz [Lx, Ly] = iħ

Is it possible measure simultaneously square of angular momentum and its x projection ( ^L2 and ^Lx )?Why? Proof.

When the commutation relationship [Lx, Ly] = iℏLz true, what does it imply about the simultaneous measurement of Lx and Ly?OPTIONS Lx​ and Ly​ cannot be measured simultaneously with certainty. Lx​ and Ly​ are compatible observables. The product of the uncertainties in Lx​ and Ly​ is zero. The product of the uncertainties in Lx​ and Ly​ is ℏ.

Consider a system of total angular momentum j=1 and the operators are given by,Choose the correct options. (Marks: 4)Calculate and , when jx = -h/2πOPTIONS = h2/8π2 and = 0 = 0 and = h2/8π2 = 2 and = h2/π2 = 0 and = h/8π2

How can the angle between the angular momentum vector ⃗ L and the z-axis be calculated in quantum me-chanics? Calculate the allowed possible values of this angle for 2p - orbital.