# Quantum physics self study

1. Sep 21, 2014

### SuperDaniel

Hello,
Quantum Physics is a topic that I didn't study in college, and, I do not know why, is calling my attention lately.
Just to mention my background, I had 2 physics courses (mechanics and electromagnetism), and I used to study from Physics 1 and 2 by David Halliday, Robert Resnick, in early the 90s. Then, Siemens, the corporation that I used to work for, sent me to leadership courses, management courses, and stuff like that... to be honest with you, I am sick of those management topics... maybe, this is the main reason to come back to science. Despite the fact I am only an engineer.

1. The Feynman Lectures on Physics (3 books): for review physics mechanic and start to learn about QM, and,
2. Quantum Mechanics by Leslie E. Ballentine, for a more specific study

I do not want to bother the forum by repeating the same questions again and again, but, just to be sure, if you have any other idea or advice, I will be more than happy to receive that from you.

2. Sep 21, 2014

### Jorriss

Given your background Ballentine seems like a crazy choice, it is far too advanced in my opinion. Zettili is a much better choice for self study given it has quality explanations and a large variety of worked problems.

3. Sep 22, 2014

Since you've only done Physics 1 & 2, you should work on strengthening your Classical Mechanics before jumping into Quantum. Perhaps, before getting Zettili for QM (here: http://tinyurl.com/zettiliqm [Broken] you could use Taylor's Classical Mechanics text (sophomore-junior level), found here: http://tinyurl.com/taylorcm [Broken] followed by some Electrodynamics: http://tinyurl.com/nh5jkdp [Broken]

Last edited by a moderator: May 7, 2017
4. Sep 22, 2014

You can jump into Zettili straight away but I do not recommend it.

5. Sep 22, 2014

### atyy

The Feynman lectures are great, but they don't give the textbook postulates and make some misleading remarks about hidden variables, as this issue was not well understood in his time. I highly recommend the Feynman lectures, because they give the insight of a great physicist, but they should be supplemented by a more conventional text like Zettili, Griffiths, Shankar, or Sakurai and Napolitano.

The presentation in these standard texts don't cover two issues (1) that there are measurements more general than projective measurements (2) interpretational issues. A reading list on generalized measurements is given in https://www.physicsforums.com/threads/measurement-theory.769143/#post-4846641. An introduction to interpretational issues is given in Landau and Lifshitz https://www.amazon.com/Quantum-Mechanics-Third-Edition-Non-Relativistic/dp/0750635398 and Weinberg https://www.amazon.com/Lectures-Quantum-Mechanics-Steven-Weinberg/dp/1107028728. Landau and Lifshitz, and Weinberg are also great standard texts on the subject. They are not usually recommended as introductory texts, because they are considered hard. My own view is that they are not that hard, because of the great clarity of thinking in these texts.

Ballentine is recommended by many here, but it is a controversial book. Unlike Feynman, this is not due to subtleties not well understood in Ballentine's time, but rather represent Ballentine's idiosyncratic personal views. So if one reads it, it is best to do so after one has learnt conventional quantum mechanics.

Last edited by a moderator: May 7, 2017
6. Sep 22, 2014

### vanhees71

First one should stress that it is a feature not a bug of textbooks on QT not to dwell on "interpretation" too much. As a beginner, you just need to understand the probabilistic meaning of the abstract objects of quantum mechanics (Hilbert-space vectors/Statistical Operators as descriptions of the state and essentially self-adjoint operators as representatives of observables) in terms of Born's rule, which is just one of the basic axioms of quantum theory. Then you can understand, how quantum theory is used to describe observations and experiments made in the real world, and that's all what's needed to test a theory against observations, and physics is precisely about this ability to test hypotheses against observations in the real world.

Everything beyond this necessary interpretation of the formalism is metaphysics and does more harm than good to the beginner. Although I agree that Ballentine's book is not suited as a first textbook to start learning quantum mechanics (exactly because there's too much discussion about interpretation issues in it that cannot be understood by beginners in the subject), I don't consider the views in this book concerning interpretation as "idiosyncratic". To the contrary, the minimal interpretation is the way quantum theory is used by practitioners of physics (or let's say by feeled 99.999% of all experimental and theoretical physicists using quantum theory): there is a formalism called quantum theory, and the minimal interpretation (of the states in terms of probabilities following Born's rule) provides the necessary link to make contact to real-world observations and experiments to test QT as a physical theory. The probalistic nature of the theory implies that it makes statements that are testable on reproducible experiments on ensembles of independently but identically prepared setups.

You don't need any more than that (no hidden variables, no Bohm, no many worlds and, particularly important, no collapse hypothesis as advocated by some flavors of the Copenhagen interpretation).

Last edited: Sep 22, 2014
7. Sep 22, 2014

### dextercioby

I concur to vanhees' remarks. I think people should start off a subject in a gentle way, but with strong background knowledge: elementary electrodynamics and Hamiltonian classical mechanics are a must for physics side, integro-differential calculus (real variable), rudiments of complex analysis and standard linear algebra (for math) should get your knowledge of QM to a medium level, which is what the majority of the graduates need.

8. Sep 22, 2014

### vanhees71

I think, the most important prerequisite for QT is classical Hamilton mechanics in Poisson-bracket notation. For the non-relativistic theory from electromagnetism electro- and magnetostaticsstatics is enough for the first steps in atomic physics. Also one should know about Fourier series and integrals and differential equations to be used in the position representation aka. wave mechanics.

9. Sep 22, 2014

### atyy

Well, Landau and Lifshitz and Weinberg are not in your 99.999%. That makes Ballentine controversial.

10. Sep 22, 2014

### SuperDaniel

Guys,
Many thanks for all your messages!!
As mentioned, I am going to review, first classical mechanics and electrodynamics.
Then I will follow with QM, as, you well mention.
As I do this in my free time, as a hobby, I will ask to you for support, again, in the near future...

11. Sep 22, 2014

### SuperDaniel

I couldn't agree more: there are some scientists as well as poets, rock n roll bands, etc. that we should read and listen to.

12. Sep 22, 2014

### vanhees71

Where do you get this impression from? Landau and Lifshitz are very clear in discussing the basic facts within the minimal interpretation. There's not much of metaphysical, unnecesary interpretational additions. It's an excelleht book on QT. I didn't recomment it for a beginner, because it's overemphasizing wave mechanics, and I prefer an approach starting with the Hilbert-space formalism, treating wave mechaniccs as the position representation. I'd suggest Sakurai to start with learning QM. Feynman is also extremely towards a minimal interpretation, even in the sense of "shut up and calculate". It's also overemphasizing wave mechanics.

Weinberg's book is great too. Concerning interpretation, he says, it's an open issue. The chapter about interpretation is quite early in the book and gives a careful analysis of the question, whether the Born rule can be derived from the othervpostulates, coming to a negative conclusion. I think, also Weinberg is at an advanced level, not suitedcas a first intro to QT, but very valuable as a book for advanced studies.

13. Sep 22, 2014

### atyy

Landau and Lifshitz, Weinberg and Sakurai are all Copenhagen-style interpretations, which one can call "minimal" or "shut-up-and-calculate". Ballentine explicitly challenges the Copenhagen-style interpretation, and so his book cannot be considered uncontroversial. In both his famous 1970 review and his book, there are deliberate deviations from the quantum mechanics of Landau and Lifshitz, Weinberg, Sakurai, Shankar, Cohen-Tannoudji, Diu and Laloe, Griffiths, Zettili, and Nielsen and Chuang.

Last edited: Sep 22, 2014
14. Sep 22, 2014

### dextercioby

Ballentine has the merit of writing a textbook (controversial because of the refutation of the standard Copenhagen interpretation (von Neumann's collapse postulate)) that will forever stand alone among the rest of the books on quantum mechanics. A future theoretical physicist MUST have this book close by.

15. Sep 22, 2014

### Jorriss

I don't understand this suggestion. Sakurai is not an introductory text for self study. He doesn't even do the hydrogen atom because it's assumed the reader has seen it.

16. Sep 23, 2014

### vanhees71

In my copy of Sakurai's textbook the hydrogen atom is treated in Sect. 3.7. I also still do not understand, where Landau and Lifshitz deviate from the minimal interpretation. If you take away the Collapse Postulate (which is totally unnecessary to begin with and then ends in the EPR desaster) you have the minimal interpretation. Landau and Lifshitz are particularly careful in describing the basic concepts already in the very first paragraph of their book. They even describe correctly the meaning of the uncertainty relation, which is not due to the disturbance of a system due to a measurement but it's due to the fact that you cannot prepare a system in a state which in general implies the determinacy of two non-compatible observables.

As I said, I'd recommend Ballentine only as a book for advanced readers, but then as the best book concerning the discussion of the various interpretations, cleaning up most of the unnecessary ballast most of all these interpretations leave in the minds of physicists. Another very good book on interpretation is

Asher Peres, Quantum Theory: Concepts and Methods, Kluwer (2002)

It's also not recommended as a book to begin with but to read to clarify the interpretation issues later.

17. Sep 23, 2014

### atyy

But Landau and Lifshitz do have the collapse postulate. This is where Ballentine deviates from LL. So if Ballentine's interpretation is "minimal", then LL (and Weinberg, Nielsen and Chuang, etc) is certainly not among them. As for EPR, if the measurement is simultaneous in one frame, it cannot be simultaneous in another frame. The collapse postulate deals with non-simultaneous measurements, and it is correct to use collapse to calculate the probabilities for such results. http://arxiv.org/abs/1007.3977

Incidentally Ballentine also got the "uncertainty principle" wrong in his 1970 review. There are several "uncertainty principles" coming from the commutation relations. The most common one is, as you say, about what states can be prepared, and is not about simultaneous measurement. However, this does not mean that simultaneous measurement of canonically conjugate observables is possible. Ballentine makes a misleading or wrong remark in his 1970 review, which again the textbooks state - canonically conjugate observables cannot be simultaneously and accurately measured on an arbitrary unknown state. In his 1970 review, Ballentine deliberately questions this standard principle, but his counterexample fails. It is true that in this case the standard theory was not fully worked out until recently, eg http://arxiv.org/abs/1306.1565. Still the standard heuristic was based on the fact that conjugate observables require different setups to measure. There were exceptions known at Ballentine's time, for special states as given by Park and Margenau. However, where Park and Margenau's exception is valid, Ballentine's is not. It's fine to make mistakes accidentally, but regarding the limitation on simultaneous measurement by non-commutation and in the questioning of the collapse postulate, Ballentine is deliberately contrary to well-known standard theory stated in many undergraduate and graduate textbooks.

Last edited: Sep 23, 2014
18. Sep 23, 2014

### SuperDaniel

Link to the book you mentioned

http://www.fisica.net/quantica/Peres - Quantum Theory Concepts and Methods.pdf

19. Sep 23, 2014

### vanhees71

Although we discuss this in the wrong subforum, I think it's a very interesting discussion. Perhaps we should open a new thread in the quantum physics forum.

Ok, I always thought from the classical textbooks on QT LL, Dirac, and even good old Sommerfeld's "Atombau und Spektrallinien" are among the books, who don't introduce the collapse argument, but I can be mistaken. I've to look it through more carefully again. But it's very clear that the collapse postulate is unnecessary and leads to the well-known contradictions which were criticized by Einstein, Podolsky, and Rosen in their famous paper.

I'm pretty sure that LL get the uncertainty relation, as it is derived in the standard way in textbooks, right. It's a statement about states. In the minimal interpretation it's clear what this means: Each state encodes the probabilities for any possible measurement on the system. This implies that I need an ensemble of equally but independent prepared systems to represent this state. The usual uncertainty relation (the Heisenberg-Robertson uncertainty relation) uses Born's rule and the positive definiteness of the scalar product of the Hilbert space to derive the following relatin about the standard deviations of observables,
$$\Delta A \Delta B \geq \frac{1}{2} \left \langle \frac{1}{\mathrm{i}} [\hat{A},\hat{B}] \right \rangle.$$
The expectation values to calculate the standard deviations and the right-hand side of the inequality have to be taken wrt. to the same (pure or mixed) state. This means you have to use one ensemble to measure observable A and another ensemble to measure B and determine its standard deviations. Then these standard deviations obey the above given uncertainty relation (supposed QT is right, and that's the case as far as we know). In this interpretation, and there is no other interpretation possible given the QT formalism, you never make a measurement of both incompatible observables on the very same system.

More recently, other kinds of measurements than these complete measurements of one observable (or a compatible set of observables) have been considered, socalled "weak or incomplete measurements", and the description of such procedures has been developed in terms of positive operator valued measures. I'm far from being an expert in this topic. As far as I understand, for such measurements, where you measure in some sense two incompatible observables both not precisely but with a certain a-priori inaccuracy. Then one can derive uncertainty-disturbance relations which are different in both their definition and their physical meaning than the Heisenberg-Robertson uncertainty relation. A while ago, I tried to discuss an easily understandable example about spin measurements on neutrons. Nobody ever responded. So it seem not to be very interesting for people in this forum. In the community it's also a quite heated debate, how to interpreat the measurement-disturbance relations; some authors contradict others claiming to the contrary that the usual Heisenberg-Robertson uncertainty relation also holds for certain types of measurement in the sense of a measurement-distrubance relation. I think, however, one has to consider each concrete experimental setup to interpret what's measured and what meaning uncertainty relations of whatever kind may have.

The original meaning of the Heisenberg-Robertson uncertainty relation is, talking about precise measurements of the two observables on then necessarily distinct ensembles, however, is very clear. Ironically Heisenberg's very first paper was wrong in misinterpreting the relation as measurement-disturbance relation. It was made clear on the example of position-momentum uncertainty and the observation of an electron by scattering of light, the "Heisenberg microscope" gedanken experiment. Very shortly after the first paper, Bohr pointed out the interpretation mistake on the very same example very clearly, coming to the conclusion that it's a property of states and has nothing to do with perturbation of the system by measurements.

In fact, if you want to experimentally check the Heisenberg-Robertson uncertainty relation with significance you have to measure both observables (on each separate ensemble) with much higher accuracy than the quantum mechanical standard deviations due to the state preparation! This underlines the more the fact that you must do the measurements of each observable on distinct ensembles.

20. Sep 23, 2014

### atyy

At least the later versions of Dirac, and also LL, do have state reduction. The problem with the traditional statement of state reduction is that it is not general enough and should include POVMs, not that we should do away with it. The Copenhagen-style minimal shut-up-and-calculate approach is to say for each observer there is a commonsense notion of "macroscopic" measuring devices and quantum systems. This division is not absolute, and different observers can place this cut in different ways. The wave function and its evolution are not necessarily real, but only a way to calculate the probabilities of outcomes of measurements. There may be a deeper theory, but we are agnostic about it until experiment falsifies quantum theory.

This is the Copenhagen-style minimal view, which Ballentine rejects. In this Copenhagen-style minimal view, there is no problem with the collapse postulate because the wave function is not real, and just a tool. As long as the tool gives the correct predictions, why should we care whether it includes collapse or not? Also, collapse is consistent with EPR. There is no problem. Although collapse is not invariant, the results of the calculations using collapse are relativistically invariant. So collapse is consistent with special relativity. Only if one somehow thinks the wave function is real and collapse is real, as Ballentine misinterprets the Dirac and LL and Weinberg minimal interpretation, then does collapse become a problem.

Yes, LL get it right and so do you. The standard uncertainty relation is a limitation on state preparation. It is true that the standard uncertainty relation is often misread as a limitation on simultaneous measurement. However, this doesn't mean there is no limitation on simultaneous measurement coming from non-commutation. Ballentine in his 1970 review tries to show a counterexample where simultaneous measurement is possible. But his counterexample fails because his "simultanouesly measured" position and momentum are not conjugate. There are special cases where simultaneous and accurate measurement of non-commuting observables is possible, but it is not possible on an arbitrary unknown state.

Last edited: Sep 23, 2014