Balancing Theory and Applications?

[yucheng]

Merely studying formalism and theory in quantum mechanics is too dry and demotivating for me. I would appreciate being able to do more practical calculations and realistic applications instead of canned problems. Is there a way to balance this theory and applications?

I have thought of doing problems books. But many problems there seem rather artificial (canned problems). It would be great if some of the toy problems actually turn out to have real applications. (simple quantum systems: square well etc)

Maybe I can explore statistical mechanics, quantum chemistry, solid state physics, condensed matter physics etc, where more practical calculations are being done.

P.S. After reading through nearly the whole of Ira N. Levine's Quantum Chesmitry, I have learned the more practical aspects of quantum mechanics for instance perturbation theory for helium and variational calculations. Also, how Helmann-Feynman theorem might be useful.

(But many applications involve relativistic QM, QFT... haha just another can of worms)

Supplement my diet with old journal articles? This goes hand-in-hand with studying the historical development of quantum mechanics, focusing on old topics, experiments and the associated calculations & data; definitely avoiding speculative interpretations. This makes transparent the motivation and development of different aspects of the theory, also rendering it more intuitive.
(Maybe not journal articles but expository articles like those in AAPT's journal haha. I really like those cited by Griffiths in his EM book. In my opinion, that's actually the most memorable part.)

P.S. Actually, using older books is advantageous in this regard, for instance Messiah's Quantum Mechanics, which starts from wave theory and how the Schrödinger equation is 'derived' from wave packets and De Broglie waves. Also, Messiah does introduce quite a lot of applications (scattering, cross section, collision).

I would like to hear your view and approach. Thanks in advance!

P.S. more examples I have actually found

Charged Particle Traps by F.G. Major. (applied EM and QM)
Atom, Molecules and Photons by Wolfgang Demtroder (rather historical!)

 

[BvU]

It would be great if some of the toy problems actually turn out to have real applications. (simple quantum systems: square well etc)

They do. You'll bump into them in a later stage and you'll be glad you did those problems thoroughly earlier, so you can concentrate on the main issue now at hand (and the lectures go a lot faster now). The square well and especially the harmonic oscillator are not canned problems. They are limiting cases of very real stuff appearing in

statistical mechanics, quantum chemistry, solid state physics

and QFT, of course

Supplement my diet with old journal articles?

That's one way (but very time-consuming). A good alternative to consider is: to go into teaching

$\$

 

[Orodruin]

I would strongly recommend against using older textbooks and old journal articles in general. While there will always be exceptions, old textbooks generally miss new developments in theory, experiment, and didactics. Old journal articles were written on what was the front line of research back then. They are generally not interesting unless your aim is to study the historical development. Research articles make very poor textbooks in general because many times the authors themselves are delving in the dark and many basic assumptions will be part of the scientific discourse of the time and therefore omitted. I’d say you are generally better off with a good modern textbook.

PS. There are many old ”bibles” and some will be worth a read. One could ask the question if this indicates textbooks were better back then. While it was probably harder and more work to publish a textbook, meaning that quality may have been more important, we must also remember that we will not know of many textbooks from back then that did not become ”bibles” simply because they fell into oblivion.

 

[yucheng]

Old journal articles were written on what was the front line of research back then. They are generally not interesting unless your aim is to study the historical development. Research articles make very poor textbooks in general because many times the authors themselves are delving in the dark and many basic assumptions will be part of the scientific discourse of the time and therefore omitted.

Maybe not journal articles but expository articles like those in AAPT's journal haha. I really like those cited by Griffiths in his EM book. In my opinion, that's actually the most memorable part.

 

[yucheng]

Old journal articles were written on what was the front line of research back then. They are generally not interesting unless your aim is to study the historical development.

How about Electron Capture by Protons Passing through Hydrogen by JD Jackson and Harry Schiff? Reading it and deciding what prerequisite knowledge one needs to learn sounds like a nice project to work on in one's free time.

 

[Frabjous]

Research papers presuppose background knowledge so you will need a solid foundation. Depending on you long term interests, you can take either the physics or chemistry paths, but you will need to spend time learning the “dry stuff”.

Since you want some old stuff …
Quantum Mechanics by Lipkin
Intermediate Quantum Mechanics by Bethe and Jackiw
Chemical Bonds by Gray https://authors.library.caltech.edu/105209/
Quantum Theory (multiple books) by Slater

Condenses matter/solid state is essentially applied quantum
Similarly for lasers/atomic and molecular physics/spectroscopy

 

[yucheng]

Depending on you long term interests, you can take either the physics or chemistry paths, but you will need to spend time learning the “dry stuff”.

Indeed, it's for the long term, hence I can slowly build up the requisite knowledge. I am aware that no matter how dry, one still has to go through it. At least it won't be as painful if one takes the time to appreciate the formalism (and not speed through!)

Thanks for the recommendations!