A particle with mass m, position r' and momentum p has angular momentum M = 7...

 

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A particle with mass m, position r' and momentum p has angular momentum M = 7 x p. (a) Evaluate {x,, M}, {Pj, Mk}, {M₁, Mk} and {M₁, M²}. (b) Consider a particle of mass m moving in a central potential V(r) = -mK/r. Recall the Runge- Lenz vector A = px M - mKf. Show that 2H {M₁, Aj} = €ijk Ak, {A₁, Aj} = m Prove using Poisson brackets that A is conserved. (Also note that A, M and H form a closed algebra under the Poisson bracket.) -tijk Mk. A particle with mass m, position r' and momentum p has angular momentum M = 7 x p. (a) Evaluate {x,, M}, {Pj, Mk}, {M₁, Mk} and {M₁, M²}. (b) Consider a particle of mass m moving in a central potential V(r) = -mK/r. Recall the Runge- Lenz vector A = px M - mKf. Show that 2H {M₁, Aj} = €ijk Ak, {A₁, Aj} = m Prove using Poisson brackets that A is conserved. (Also note that A, M and H form a closed algebra under the Poisson bracket.) -tijk Mk.

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The detailed answer for the above question is provided below a a Mk 0 Pj Mk jkp Mj Mk jklMl M M 0 b Mi Aj ijkPkMjmKij EijkAk Ai Aj ijkPkPjmKij 2Hmijk ... View the full answer