(Solution) - A particle moves in a potential V r V0e 2 -(2025 Original AI-Free Solution)

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A particle moves in a potential V (r) = ?V0e??2r2.
(a) Given L, find the radius of the stable circular orbit. An implicit equation is fine here.
(b) It turns out that if L is too large, then a circular orbit actually doesn?t exist. What is the largest value of L for which a circular orbit does indeed exist? What is the value of Veff (r) in this case?