Quantum Thoughts on Albrecht Lindner's A Complete Course on Theoretical Physics?

[Geofleur]

Has anyone had experience with Albrecht Lindner's book, A Complete Course on Theoretical Physics?

https://www.springer.com/la/book/9783030043599

It looks like it covers a lot of material, and I'm wondering what people here think of it, especially the chapters on quantum theory.

 

[jedishrfu]

This book is pretty new so you might not get any responses for it.

Perhaps you could lookup other books by this author to see how well they were rated on Amazon.

I checked but it seems he has no other books in English and none have any reviews.

 

[dextercioby]

Has anyone had experience with Albrecht Lindner's book, A Complete Course on Theoretical Physics?

https://www.springer.com/la/book/9783030043599

It looks like it covers a lot of material, and I'm wondering what people here think of it, especially the chapters on quantum theory.

It starts badly with „the wave-particle” duality, but, if you skip that small section, it is a good read.

 

[Geofleur]

What didn't you like about that section?

 

[dextercioby]

It should not be present in a textbook: The wave-particle duality is a phrase and a concept born 90 years ago and, after the correct formulation of quantum mechanics with appropriate concepts (systems, states, observables, observers), it became obsolete (basically, it creates the interpretation that a system properly described by quantum mechanics can be viewed from the perspective of classical physics, in which waves and particles are fundamental concepts).

 

[Geofleur]

Now we just say that a particle corresponds to a localized wave, right?

I have to admit, I'm still a bit fuzzy about one aspect of this idea. Back in college, I was taught that we only ever measure particles, as when a detector screen lights up only at individual points in the double slit experiment. To explain this phenomenon, people sometimes talk about collapse of the wave function. It's as if there is a wave until a measurement is made, and then there's a particle (or not). If someone were to mention this experiment and ask me whether it shows wave-particle duality, how should I respond? I'm not sure whether I should start a separate thread... this question might be a big can of worms to open!

Later edit: On doing a search, I can see that this topic has been beaten to death here! I'll have to go over all that and see if I understand it better.

Even later edit: After some reading, it seems like a local interaction between the detector and the electron's underlying quantum field should not be construed as a "particle", or at least not talked about as if it were somehow inconsistent with wave behavior. Maybe I'd been understanding the idea of duality too... charitably.

 

[vanhees71]

I'd say from the most fundamental point of view we have today particles are described by quantum fields. It's indeed important to keep in mind that the particle-like phenomena are due to the interaction of quantum fields with the macroscopic measurement devices (which themselves are, at least in principle, many-body quantum-field theoretically describable systems). E.g., photons (i.e., single-quantum-Fock states of the electromagnetic field) have no position observable to begin with. When detected with a position-resolving device (on a fundamental level usually somehow related to the photoelectric effect), it appears as a localized excitation of the detector material, but that's no contradiction but well understood.

The didactical question, how to present quantum theory is however unsolved for me presonally. I'm a strong proponent for the non-historical approach, starting with simple phenomena, presented from the point of view of modern quantum theory. The problem with this approach, however, is that it's hard to start in this way because if you want to start with the Stern-Gerlach experiment and spin-1/2 two-dimensional Hilbert space, you don't have the notion of spin at hand since this needs the very notion of modern quantum theory to get it right. In the previous semester I have given an introductory QM lecture to physics-teacher students. There I decided, I use the polarization observable of classical electromagnetic wave and polarization filter ("polaroids foils") as heuristic starting point for the description of idealized von Neumann filter measurements, introducing the photon in a quite qualitative way, but emphasizing that the naive idea of localized particles is flawed and that rather the wave picture is a better heuristics but also not completely correct. From this you can build the fundamental idea of modern QM to use a Hilbert space to define states and observables with the minimal statistical interpretation for the physical state (a la Born). In my opinion the interpretational problems of quantum theory (if you agree that there are such problems, which I doubt as a physicist, but that's a personal opinion) can only be discussed after a thorough mathematical introduction to the theory. There's no way to do QT (if not even physics as a whole) than this solid mathematical foundation.

The historical approach is particularly bad for introductory QM, because it overemphesizes the wrong concepts of the "old quantum theory", i.e., Einstein's flawed particle picture of photons and Bohr's self-contradictory atomic model with discretized classical orbits of electrons around atomic nuclei. The problem with this is that the pictures are not only empirically wrong (except for the energy levels of the hydrogen atom and the harmonic oscillator, which systems are so restricted by the huge dynamical symmetries of these special systems that it's almost impossible to get them wrong in any reasonable theory, there's no single other successful application of Bohr-Sommerfeld quantization) but provide wrong qualitative pictures about what's going on on the quantum level. The only way to get intuition is to get used to mathematical thinking and its application to the quantum phenomena.

Don't get me wrong: I also think that some knowledge of the history of physics is very important for any physicist, and it's of great merit to study it, but it's the wrong way to introduce physics in the intro theoretical-physics lectures. After you have learned the modern theory, it's however very good to study how the physicists came to these theories and models as a result of an interplay of experiments and model building by theorists.

 

[Geofleur]

I really like the idea of presenting the modern formalism the first time around and getting to history later, and starting with light polarization makes a lot of sense to me as well (maybe I'll try that this time around!). In fact, I've been reading all these different presentations of QM because I want to find a clear way to present it that is also consonant with the QFT perspective (and to understand the latter better myself).

photons (i.e., single-quantum-Fock states of the electromagnetic field

I'm still a little unclear about the nature of the Fock states. They seem to be symmetrized (Boson) or anti-symmetrized (Fermion) tensor products of Hilbert spaces? Also, are the components of the Fock space always explicitly formulatable? In QFT texts, I find a lot of kets with occupation number labels but not (so far) any explicit mathematical expressions for the single particle states. There are certainly explicit expressions for the field operators, and that's comforting!

I was also wondering whether it might be a good idea to do second quantization right after the harmonic oscillator, and present that as a kind of non-relativistic QFT. So the single particle states would be expressions involving Hermite polynomials; an occupation number ket would be some kind of symmetrized product of single particle states. Would that work? If a student asks me for a mathematical expression for the quantum field in this case, would it just be the expressions for the raising and lowering operators?

I realize that's a lot of questions! Usually when I learn something, I work through all the little details, but that has the unfortunate side effect of taking a long time. I'm trying (for the first time ever) to just read things, get an idea, and go back later to work out details; it's led to a lot of questions.

 

[vanhees71]

Yes, I think that's a very good approach. If I had to give a lecture on many-body physics, I'd present many-particle systems in QM 1 in the following way (after having covered the 1st quantized version for one particle, including spin):

(a) Consider a two-particle system in 1st quantization and discuss the necessity for symmetrization and anti-symmetrization for the case of indistinguishable praticles. Of course, for 2 particles there are only these two possibilities to describe indistinguishable particles. So one also has to discuss at least a three-particle system to see that it is an additional assumption that all many-particle states of indistinguishable N-particle systems are built by either totally symmetrized or antisymmetrized tensor products of $N$ single-particle states.

(b) Then introduce the creation an annihilation operators for many-body Fock bases, referring indeed to the example for the harmonic oscillator. This has two advantages: (i) For the case that there are no number-changing interactions this "2nd-quantization approach" delivers the same results as the 1st-quantization approach to many-body systems with fixed particle number, but it makes treatment of the Bose/Fermi (anti-)symmetrization of the bases much easier to handle. (ii) it's possible to treat systems with non-conserved particle number. In non-relativistic physics that's as important as in relativistic physics since it provides the often applicable possibility to describe many-body systems of strongly interacting particles in terms of socalled quasiparticles, i.e., quantized collective excitations of the many-body systems like phonons in solids.

 

[Geofleur]

Alright, that's how I'll approach it - thanks!