Principles of Quantum Mechanics · Problem 7.4.8

The Path Integral Formulation of Quantum Theory — R. Shankar

Physics — Quantum Mechanics · angular-momentum-quantization

Problem

Consider the three angular momentum variables in classical mechanics: lx=ypz−zpyl_x = yp_z - zp_y ly=zpx−xpzl_y = zp_x - xp_z lz=xpy−ypxl_z = xp_y - yp_x (1) Construct LxL_x, LyL_y, and LzL_z, the quantum counterparts, and note that there are no ordering ambiguities. (2) Verify that {lx,ly}=lz\{l_x, l_y\} = l_z [see Eq. (2.7.3) for the definition of the PB]. (3) Verify that [Lx,Ly]=iℏLz[L_x, L_y] = i\hbar L_z.

Related theory

Browse the problem library