(a) For a single particle show directly (that is, by direct evaluation of the Poisson brac...

(a) For a single particle show directly (that is, by direct evaluation of the Poisson brackets), that if u is a scalar function only of r2, p2, and r · p, then

 

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(b) Similarly show directly that if F is a vector function,

 

where u, v, and w are scalar functions of the same type as in part (a), then