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 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…