Mathematical Field Notes

Archive for November 2012

UCL Geometry and Topology Open Day talk: Floer theory

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These are the notes from the twenty minute talk I’m going to give at the UCL Geometry and Topology Open Day for prospective PhD students (November 14th 2012). For those who are interested in reading more, check out Milnor’s book on Morse theory and Atiyah’s early survey paper on Floer theory.

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Written by Jonny Evans

November 13, 2012 at 9:37 pm

Why Schrödinger’s equation?

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“Why this equation?”

I recently overheard someone ask this about Schrödinger’s equation. The answer they received was, for me, unsatisfying. “Because it agrees with experiment.” Of course, that answers perfectly why the equation was adopted by future generations of physicists and indeed the calculation of the spectrum of atomic hydrogen from the energy eigenvalues of the Schrödinger operator is one of the most convincing and wholesome computations a young physicist can do. But the question that was left unanswered, the question I believe was being asked, was: “Why did Schrödinger write this equation down? Why not something else?” I don’t believe for a second that Schrödinger sat down with an array of different equations and worked out what each of them predicted about hydrogen before he found the one that fit…

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Written by Jonny Evans

November 5, 2012 at 10:18 pm