The Hamilton function for a point particle moving in a central potential is given by p? H + a|x|". 2m Consider the vector A = p x L+ ma where L is the angular momentum of the particle. (a) Calculate the Poisson bracket {H, Ar}, where A is the k-th component of the vector A. (b) Determine the value of the exponent n for which the vector A becomes a conserved quantity.
The Hamilton function for a point particle moving in a central potential is given by p? H + a|x|". 2m Consider the vector A = p x L+ ma where L is the angular momentum of the particle. (a) Calculate the Poisson bracket {H, Ar}, where A is the k-th component of the vector A. (b) Determine the value of the exponent n for which the vector A becomes a conserved quantity.
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Transcribed Image Text:The Hamilton function for a point particle moving in a central potential is given by
p?
H
+ a|x|".
2m
Consider the vector
A = p x L+ ma
where L is the angular momentum of the particle.
(a) Calculate the Poisson bracket
{H, Ar},
where A is the k-th component of the vector A.
(b) Determine the value of the exponent n for which the vector A becomes a conserved
quantity.
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