Recent content by Meden Agan

  1. M

    I Schrödinger equation and classical wave equation

    Yes, but I mean: the classical wave equation has two derivatives in time and two derivatives in position; the Schrödinger equation has only one derivative in time, not two. That is different. Yes?
  2. M

    I Schrödinger equation and classical wave equation

    Yes. AFAIK, Schrödinger developed his equation through an admirable reverse engineering operation, starting from the analogy between the eikonal equation of geometric optics and Hamilton-Jacobi's equation of classical mechanics. In practice, he found the theory corresponding to wave optics in...
  3. M

    I Schrödinger equation and classical wave equation

    Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact...
  4. M

    How can we teach students the difference between sequences and series?

    Sequences and series are related concepts, but they differ extremely from one another. I believe that students in integral calculus often confuse them. Part of the problem is that: Sequences are usually taught only briefly before moving on to series. The definition of a series involves two...
  5. M

    Prove that the integral is equal to ##\pi^2/8##

    @fresh_42 Did you get something new?
  6. M

    Is mathematics invented or discovered?

    The question ‘is mathematics invented or discovered?’ is a much-debated issue in the philosophy of mathematics. It is a classic. I would like to know what you think about it. Below is my view. IMO, the question ‘is mathematics invented or discovered?’ pits two equally plausible intuitions...
  7. M

    Prove that the integral is equal to ##\pi^2/8##

    I don't see how that helps either. Let me know if you get anything useful, I'm stuck.
  8. M

    Prove that the integral is equal to ##\pi^2/8##

    @fresh_42 Did you get something new? If the answer is no, let's go ahead to analyze the solution on MSE.
  9. M

    Prove that ##\lim\limits_{x \to \infty} f(x) = 0##

    Mhm, could you outline what's unclear step by step? Hope I can provide a detailed clarification.
  10. M

    Prove that ##\lim\limits_{x \to \infty} f(x) = 0##

    Let ##f(x)= \min\limits_{m, n \in \mathbb Z} \left|x- \sqrt{m^2+2 \, n^2}\right|## be the minimum distance between a positive real ##x## and a number of the form ##\sqrt{m^2 + 2 n^2}## with ##m, n## integers. Let us consider a radius ##R## and let us consider the set ##S_R## of integer points...
  11. M

    Prove that the integral is equal to ##\pi^2/8##

    I agree. Your ideas are always excellent, but unfortunately there's nothing we can do. The form in post #86 made me hopeful. But unfortunately nothing came of it.
  12. M

    Prove that the integral is equal to ##\pi^2/8##

    Sad. I can't believe that is the only possible solution to the integral.
  13. M

    Prove that the integral is equal to ##\pi^2/8##

    Any significant developments? I've come up with a heuristic argument, but I'm becoming more and more convinced that is not correct either.
  14. M

    Prove that the integral is equal to ##\pi^2/8##

    IMO, the expression $$2 \int\limits_{0}^{1} \frac{\alpha(z)}{\sqrt{1-z^2}} \, \mathrm dz = \frac{\pi^2}{8}$$ is the best way of representing the integral. Perhaps it is enough to choose ##\alpha(z)## so that the integrand is symmetric in the interval ##(-1, 1)##, like the original function? The...
  15. M

    Prove that the integral is equal to ##\pi^2/8##

    Mhm, but unfortunately that derivative is frankly unmanageable. We seem to have complicated the integral again.
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