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?
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...
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...
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...
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...
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...
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.
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...