Question

 

Obtain the radial action and the angular action variables. Hence, express the total action.

19 Jan 2026
Answer :
Word Count : 216
For a particle in a central potential (V(r)), the Hamiltonian in plane polar coordinates is: [ H = \frac{p_r^2}{2m} + \frac{p_\theta^2}{2 m r^2} + V(r), ] where (p_r) and (p_\theta) are the radial and angular momenta. Step 1: Angular action variable (J_\theta) The angular momentum is conserved: (p_\theta = L). The angular action variable _______ ____ ________ ______ _____ _______ _____ ______.
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