Question

Nested commutators. Someone gives you the identity e*Ae-+ = A + [L.A] + ;LLA] +L. [L. (L. A] + +.. where A and L are operators. For all parts let L L., and A = &. %3D [5pts](a) Evaluate the commutator in the second term, [1., 8]. (You should use that &, P] = ihôy. and that L, = £py-ŷPx.) %3D [5pts](b) Evaluate the commutators in the 3rd term: [L [L., £]

please help with this question,full details please

Answer 1

9. Anwen 5 (al [laz, x] = [x by- y bx ,x ] => [py, 2] + [x, XJ Py -y [bx, x] + [J, 2 bx - sme [xibi] = insis so [by, x) = 0 [ x, 3c] =0 [box] =-it, [4, x3=0 [Lz ,&] =-ity (b 1 [L₂ , [[z ,x] ] = [lz ,city] =-ih [ 2₂ 14] so [lz,y] =[xby-y bx, y] =- 1hoc [L2, [tz ,x]] =-ih (inx) = -ħod / [lz, [Lz ,x]] =- ² x