My professor and I have been working on a proof of Bertrand's Theorem using perturbative methods. We have arrived at a solution yielding 1/r^3, which we had presumed to be an incorrect result. While I'm new to his research, I have been obsessing over finding reconciliation or a SPoF.
However, after reading the last comment on the first reply to this particular SE post, I am reconsidering this result: [ An intuitive proof of Bertrand's theorem ]
Can somebody elaborate on what @mmesser314 is talking about? I haven't seen a perturbation-based derivation lead to a 1/r^3 result in the literature I've encountered. I'd really appreciate it.
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