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Solution for differential equation
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[QUOTE="kuruman, post: 6853403, member: 192687"] You have written a three-dimensional equation for what is essentially a one-dimensional problem because the potential depends on ##r## only. For that reason, I think it is safe to assume that angular momentum is conserved, write the standard energy conservation equations, one for each region, used in central force problems and see where it takes you. You will have to figure out how to quantify the "kick" that the particle receives at the boundary. I have not solved this problem, but that would be my approach. Your friend is correct. If the particle has energy less than ##V_0##, it will not penetrate (classically) the potential, i.e. it will bounce off with no energy loss. This sounds like scattering off a hard sphere to me. [/QUOTE]
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Solution for differential equation
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