A Deranged Mathematician Does Quantum Mechanics

Years ago, when I was finishing a double-major in math and physics, I wrote my undergraduate thesis as a guide to the mathematician trying to learn quantum mechanics. I have come back to it periodically since, tweaking and streamlining my main argument: if you approach quantum mechanics from the right, functional-analytic perspective, all of the weird peculiarities of the mathematical framework (Hilbert spaces, self-adjoint operators, the Schrödinger equation, etc.) don't just start to make sense... one gets a powerful feeling that this was really the only possible definition that could have worked, in light of the existing experimental observations. Whether that is useful from the perspective of the scientific method is perhaps questionable (physics is and always should be grounded in experiment, first and foremost), but as a pedagogical tool that helps us better conceptualize and even extend the theory, I think that it has some benefit. So, if you have ever wanted to learn a little bit about quantum, or if you just want to see how fairly advanced and seemingly abstract mathematics can be applied, this article may be of interest to you. Read the full post (for free) on Substack: A Deranged Mathematician Does Quantum Mechanics .