9. Poisson brackets with angular momentum:(a) Calculate the following Poisson brackets of the components of ~r and ~p : - {x, z}, {y, py}, {z, py}.(b) Calculate all the Poisson brackets of the components of ~r and ~p with the components ofthe angular momentum ~l = ~r × ~p (for example, {x, lx}, {x, ly}, {px, lx} ... etc.). Use theLevi-Civita completely antisymmetric tensor ijk such that li = ijkrjpk.(c) Prove that {lx, ly} = lz for all cyclic permutations of lx, ly, lz. 9. Poisson brackets with angular momentum:(a) Calculate the following Poisson brackets of the components of 'and p: - {x, z}, {y, Py}; {z, Py}.(b) Calculate all the Poisson brackets of the components of and p with the components ofthe angular momentum l= 7x 7 (for example, {x,l½}, {x,ly}, {px,lz} ... etc.). Use theLevi-Civita completely antisymmetric tensor €ijk such that l; = €ijkrjPk -(c) Prove that {lz, ly} = lz for all cyclic permutations of l, ly, lz.

a) The Poisson bracket of x,z, x,z=∂x∂x∂z∂px-∂z∂x∂x∂px+∂x∂z∂z∂pz-∂z∂z∂x∂pz=0 The Poisson bracket of…

9. Poisson brackets with angular momentum: (a) Calculate the following Poisson brackets of the components of r'and p: - {x, z}, {y,Py}, {z, Py}. (b) Calculate all the Poisson brackets of the components of ī and p with the components of the angular momentum l = 7 x p (for example, {x, l4}, {x,ly}, {Px,lz} Levi-Civita completely antisymmetric tensor €ijk Such that li = €ijk" jPk• (c) Prove that {l,ly} = lz for all cyclic permutations of ly, ly, lz. etc.). Use the ...

9. Poisson brackets with angular momentum: (a) Calculate the following Poisson brackets of the components of r'and p: - {x, z}, {y,Py}, {z, Py}. (b) Calculate all the Poisson brackets of the components of ī and p with the components of the angular momentum l = 7 x p (for example, {x, l4}, {x,ly}, {Px,lz} Levi-Civita completely antisymmetric tensor €ijk Such that li = €ijk" jPk• (c) Prove that {l,ly} = lz for all cyclic permutations of ly, ly, lz. etc.). Use the ...