Recent content by pabloweigandt

Can I say, by any means, that a "brain wave" is, in fact, a wave of some kind?

Is there any specialize articles that talk about how Astronomy can help learning Math and Physics? In particular, how observational astronomy can help in the learning process of Math and Physics.

If they are a basis for a separable Hilbert space, how come they are not countable? I was thinking that maybe you can generate all the uncountable position eigenkets with a countable basis. And also I am trying to understand how it is possible to avoid rigged Hilbert spaces to treat QM...

Can I conceive a countable position basis in Quantum Mechanics? How can I talk about the position basis in the separable Hilbert space?

Just above, in chapter six of Hall it says "Thus, the notion of a direct integral gives a rigorous meaning to the notion of “eigenvectors” that are not actually in the Hilbert space". You need to recognize "eigenvectors" outside the Hilbert space anyway. Are these "generalized eigenvectors" a...

How is that "rigorous treatment" without rigged Hilbert space?

That's right. But for example, if you mention the Hilbert space, and then you use the Dirac delta distribution, and you don't mention the rigged Hilbert space, I think that something is missing, and you need to justified things like in Ballentine or any other means. Of course, you can talk about...

Thanks. I will review in detail all the comments and references that you posted.

What I mean is why some authors avoid mentioning or treat rigged Hibert space when they suppose to be formulating QM in a rigorous mathematical context.

In Quantum Mechanics, how can you justify the use of distributions like the delta functional without introducing a rigged Hilbert space? I see that some texts do not make any reference to this subject.

Ok. I am new to this. I found the definition of "hijacking". You are right and I am so sorry. I would be grateful If anyone can tell me where to post this kind of topics.

"Space is expanding" will mean that I know what space is. And that there is no difference between two galaxies that are getting apart at superluminal speeds (if it is true that I can use the term "speed" or "velocity" in this case) and two cars moving apart each other.

I think that, at the end, it is absolutely necessary to understand what "space" is or what "space-time" is, and we need to stop the abuse of terminology like "matter curve spacetime" or "space is expanding" or "spacetime is expanding" or things like that.