I’ve been slacking, so bye for now, and see you later!

Recently, as I was putting finishing touches in my mind as to how to present the topic of the product states vs. the entangled states in QM, I came to realize that while my answer to that aspect has now come to a stage of being satisfactory [to me], there are any number of other issues on which I am not as immediately clear as I should be—or even used to be! That was frightening!! … Allow me to explain.

QM is hard. QM is challenging. And QM also is vast. Very vast.

In trying to write about my position paper on the foundations of QM, I have been focusing mostly on the axiomatic part of it. In offering illustrative examples, I found, that I have been taking only the simplest possible examples. However, precisely in this process, I have also gone away, and then further away, from the more concrete physics of it. … Let me give you one example.

Why must the imaginary root of the unity i.e. the $i$ appear in the Schrodinger equation? … Recently, I painfully came to realize that I had no real good explanation ready in mind.

It just so happened that I was idly browsing through Eisberg and Resnick’s text “Quantum Physics (of Atoms, Molecules…).” In my random browsing, I happened to glance over section 5.3, p. 134, and was blown over by the argument to this question, presented in there. I must have browsed through this section, years ago, but by now, I had completely forgotten anything about it. … How could I be so dumb as to even forget the fact that here is a great argument about this issue? … Usually, I am able to recall at least the book and the section where an answer to a certain question is given. At least that’s what happens for any of the engineering courses I am teaching. I am easily able to rattle off, for any question posed from any angle, a couple (if not more) books that deal with that particular aspect best. For instance, in teaching FEM: the best treatment on how to generate interpolation polynomials? Heubner (and also Rajasekaran), and only then Zienkiwicz. In teaching CFD: the most concise flux-primary description? Murthy’s notes (at Purdue), and only then followed by Versteeg and Mallasekara. Etc.

… But QM is vast—a bit too vast for me to recall even that much about answers, let alone have also the answers ready in my mind.

Also, around the same time, I ran into these two online resources  on UG QM:
1. The course notes at Reed (I suppose by Griffiths himself): [^] and [^]
2. The notes and solved problems here at “Physics pages” [^]. A very neat (and laudable) an effort!

It was the second resource, in particular, which now set me thinking. … Yes, I was aware of it, and might have referred to it earlier on my blog, too. But it was only now that this site set me into thinking…

As a result of that thinking, I’ve decided to do something similar.

I am going to start writing answers at least to questions (and not problems) given in the first 12 or 14 chapters of Eisberg and Resnick’s abovementioned text. I am going to do that before coming to systematically writing my new position paper.

And I am going to undertake this exercise in place of blogging. … It’s important that I do it.

Accordingly, I am ceasing blogging for now.

I am first going to take a rapid first cut at answering at least the (conceptual) questions if not also the (quantitative) problems from Eisberg and Resnick’s book. I would be noting down my answers in an off-line LaTeX document. Tentatively speaking, I have decided to try to get through at least the first 6 chapters of this book, before resuming blogging. In the second phase, it would be chapters 7 through 11 or so, and the rest, in the third phase.

Once I finish the first phase, I may begin sharing my answers here on this blog.

Believe me, this exercise is necessary for me to do.

There certainly are some drawbacks to this procedure. Heisenberg’s formulation (which, historically, occurred before Schrodinger’s) would not receive a good representation. However, that does not mean that I should not be “finishing” this (E&R’s) book either. May be I will have to do a similar exercise (of answering the more conceptual or theoretical questions or drawing notes from) a similar book but on Heisenberg’s approach, too; e.g., “Quantum Mechanics in Simple Matrix Form” by Thomas Jordan [^]. … For the time being, though, I am putting it off to some later time. (Just a hint: As it so happens, my new position is closer—if at all it is that—to the Schrodinger’s “picture” as compared to Heisenberg’s.)

In the meanwhile, if you feel like reading something interesting on QM, do visit the above-mentioned resources. Very highly recommended.

In the meanwhile, take care, and bye for now.

And, oh, just one more thing…

…Just to remind you. Yes, regardless of it all, as mentioned earlier on this blog, even though I won’t be blogging for a while (say a month or more, till I finish the first phase) I would remain completely open to disclosing and discussing my new ideas about QM to any interested PhD physicist, or even an interested and serious PhD student. … If you are one, just drop me a line and let’s see how and when—and assuredly not if—we can meet.

Which Song Do You Like?

Check out your city’s version of Pharrell Williams’ “Happy” song. Also check out a few other cities’. Which one do you like more? Think about it (though I won’t ask you the reasons for your choices!)

OK. Take care, and bye (really) for now…

Explicit vs. implicit FDM: reference needed

The following is my latest post at iMechanica [^]:

“The context is the finite difference modeling (FDM) of the transient diffusion equation (the linear one: $\dfrac{\partial T}{\partial t} = \alpha \dfrac{\partial^2 T}{\partial x^2}$).

Two approaches are available for modeling the evolution of $T$ in time: (i) explicit and (ii) implicit (e.g., the Crank-Nicolson method).

It was obvious to me that the explicit approach has a local (or compact) support whereas the implicit approach has a global support.

However, with some simple Google searches (and browsing through some 10+ books I could lay my hands on), I could not find any prior paper/text to cite by way of a reference.

I feel sure that it must have appeared in some or the paper (or perhaps even in a text-book); it’s just that I can’t locate it.

So, here is a request: please suggest me a reference where this observation (about the local vs. global support of the solution) is noted explicitly. Thanks in advance.

Best,

–Ajit

[E&OE]”

Self-explanatory, right?

[E&OE]

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An introductory course on CFD—3

The Beamer slides for Lecture # 3 are uploaded; see here [^].

This lecture is not directly concerned with CFD, or for that matter, even with fluid dynamics proper. It instead concerns itself with some material that is pre-requisite to both. Namely, the topic of tensors. However, Indian universities don’t cover this topic very well during the earlier, pre-requisite courses—esp. at the UG level. So, I decided to throw in some formulae and a few points concerning vectors and tensors, that’s all.

The material for this lecture, thus, is totally “extra” (at least in a course on CFD). The treatment here is, therefore, very cursory. The idea was to give students at least some background into these topics, by way of a rapid review.

As usual, feel free to point out errors and offer criticism.

Further, this topic being challenging to present to a newcomer in a brief manner, this lecture is the one where I am confident in the least. (At least, it’s the first lecture of this kind.) So, any suggestions for a better presentation would be highly appreciated (though, given my experience of this blog, really speaking, I don’t expect any comments to come in, anyway.)

All the same, I am happy that so much of typing in of these equations is, finally, out of the way!

“Enjoy”!

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A Song I Like:

I still have not yet reviewed and taken a decision as to the song I like, also for this time round.

So, this section will continue to remain suspended.

[E&OE]

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An introductory course on CFD—2

The Beamer slides for Lecture # 2 are uploaded, here [^].

As usual, feel free to point out errors and offer criticism.

[I did spot a few typos in the Lecture # 1 (see previous post). These are being corrected, and an improved version will be uploaded some time later.]

Update on 2015.07.16:

For the convenience in updating, I have created a separate page at my personal Web site; it holds all the links to the material for this CFD course.

* * * * *   * * * * *   * * * * *

A Song I Like:

I have not yet reviewed and taken a decision as to the song I like.

So, this section will remain suspended, for the time being.

[E&OE]

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