Recent content by Meden Agan

Sure. But if you differentiate ##\Theta(t) = \arcsin \left(\sqrt{E(t)}\right)## with respect to ##t##, you don't obtain the expression for ##\Theta'(t)## given by ##(3)##.

@fresh_42 I found a solution to this integral here. Does it convince you? I can't understand how they derived equation ##(3)## from equation ##(2)##.

Sorry, I wasn't clear from the very start. In my academic studies, I've heard some professors say that Schrödinger's equation is a wave equation, and others say that Schrödinger's equation is a diffusion equation. I was confused by the terminology. I think @PeterDonis is right when he asserts this:

My primary reference is Variational Principles in Dynamics and Quantum Theory by Yourgrau and Mandelstam. It's possible to see an outline of Schrödinger's original arguments for the time-independent Schrödinger equation in section 8 of Field's paper Derivation of the Schrödinger equation from...

These paragraphs.

I think you're right. So, although my original question was different and vague, I'd like to analyze some technicalities of Schrödinger's equation. Is what I said in post #30 correct?

Everything you say is correct. However, I can't conclude that Schrödinger's equation is completely different from the classical wave equation. What we know since Lagrange is that the eikonal equation governs the geometric limit of wave optics. At the same time, the equation of mechanical...

IMO, the reason why Schrödinger's equation for matter waves is first order in ##t## and the classical electromagnetic wave equation is second order in ##t## is hidden in what I wrote in post #8. It's already found in the particle counterpart: the structure of geometric optics is presymplectic...

When I receive a response to this about my interpretation of post #8, I'll proceed to step three. That's what's bothering me the most.

Yes, I agree. Note that in the Klein-Gordon equation, mass is also present. Also note that there are three spatial components. The spatial part is a Laplacian, while the first-order operator is a gradient: it is not true that ##\left(\dfrac{\mathrm d}{\mathrm dt}-\nabla_r...

I agree. I was very sloppy there.

@PeterDonis Step two. In post #1, I said: 'As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order'. Well, what does this difference in the distinction between the classical wave equation and Schrödinger's equation imply...

I strongly agree.

Clear, agreed. However, could you analyze specifically all the points in message #12? IMO, what I said involves a contradiction. Therefore, I'd like to clarify.

Well, I think I gave some context in post #1. It's a tricky question. Is Schrödinger's equation a wave equation or not? There are similarities with the classical wave equation, but also many differences that make it a heat/diffusion equation. Let's take it one step at a time. In post #1, I...