Is Landau's book on QM suitable for undergraduates?

[Joker93]

Hello,i am just starting to learn Quantum Mechanics in the university at an underdrad level. I know there are a lot of great introductory books out there but i just saw that Landau's book on non-relativistic quantum mechanics has great reviews but upon seeing it,i was overwhelmed by the mathematical rigor of the book.Now,this is a good thing but it could be bad also.I don't want to struggle with difficult maths and to sacrifice my physical understanding.
So it all comes down to whether this book is suited for undergraduate students or just graduate students.
So,what do you think?

 

[micromass]

So you never took QM before? Then Landau is not suitable at all.

 

[atyy]

Landau's remarks on interpretation are very valuable, so one can just read the English and skip the maths on first pass. You can use some other book for the maths, like French and Taylor, Griffths, or Sakurai.

 

[Joker93]

So you never took QM before? Then Landau is not suitable at all.

No,this is my first course on QM.I want to learn physics with a lot of intuition but also i want to learn the full mathematics behind each subject.What i am thinking is that it may be too much at this time

 

[Joker93]

Landau's remarks on interpretation are very valuable, so one can just read the English and skip the maths on first pass. You can use some other book for the maths, like French and Taylor, Griffths, or Sakurai.

I also have Griffith's textbook.Doesn't it offer the same intuition as Landau's textbook?

 

[atyy]

I also have Griffith's textbook.Doesn't it offer the same intuition as Landau's textbook?

There are two sorts of intuition. First, the interpretation of the mathematical formalism in terms of "true" reality. In the standard Copenhagen interpretation of quantum mechanics, the wave function is not necessarily "truly" real, and the formalism is just a means to predict the outcome of experiments. So one must have an external common-sense or "classical" or "macroscopic" observer who intuitively knows what is "truly" real. The need for this classical observer or classical world is stressed by Landau and Lifshitz, which I don't think Griffiths emphasizes.

The second type of intuition is that even though at the level of "true" reality, the wave function is not necessarily "truely" real, and just a tool to calculate outcomes, in fact we can treat it as real (ie. if it is not "truely" real, we bluff ourselves to easily calculate experimental predictions). This sort of intuition is found widely in books of quantum mechanics, including Griffiths. For example, the notion that a pure state is the complete specification of the state of an individual system, and that the wave function collapses when a measurement is made, both belong to this second type of intuition.

 

[Joker93]

There are two sorts of intuition. First, the interpretation of the mathematical formalism in terms of "true" reality. In the standard Copenhagen interpretation of quantum mechanics, the wave function is not necessarily "truly" real, and the formalism is just a means to predict the outcome of experiments. So one must have an external common-sense or "classical" or "macroscopic" observer who intuitively knows what is "truly" real. The need for this classical observer or classical world is stressed by Landau and Lifshitz, which I don't think Griffiths emphasizes.

The second type of intuition is that even though at the level of "true" reality, the wave function is not necessarily "truely" real, and just a tool to calculate outcomes, in fact we can treat it as real (ie. if it is not "truely" real, we bluff ourselves to easily calculate experimental predictions). This sort of intuition is found widely in books of quantum mechanics, including Griffiths. For example, the notion that a pure state is the complete specification of the state of an individual system, and that the wave function collapses when a measurement is made, both belong to this second type of intuition.

So,it is good if one has read books that treat QM in both intuitive ways.But the question remains,is Landau too much for me at the moment?

 

[atyy]

So,it is good if one has read books that treat QM in both intuitive ways.But the question remains,is Landau too much for me at the moment?

One doesn't need to read all of Landau to benefit from it, just the introductory chapter. There are many good books on quantum mechanics, and starting with an easy one like French and Taylor, or Griffiths is good. Basically, the subject is well-understood, and you should just pick a standard text and check out any others for alternative explanations when you run into difficulty.

 

[micromass]

No,this is my first course on QM.I want to learn physics with a lot of intuition but also i want to learn the full mathematics behind each subject.What i am thinking is that it may be too much at this time

You cannot have both in QM, especially with a first course in QM. The full mathematics can be very difficult and will obscure the intuition. While on the other hand, a book like Griffiths might be very intuitive, but isn't very mathematically rigorous.

Yes, Landau (and other mathematically advanced QM books) are too much for now. I would go with a book like Zettili first. Then you can go on to Ballentine for a more mathy account.

 

[Joker93]

You cannot have both in QM, especially with a first course in QM. The full mathematics can be very difficult and will obscure the intuition. While on the other hand, a book like Griffiths might be very intuitive, but isn't very mathematically rigorous.

Yes, Landau (and other mathematically advanced QM books) are too much for now. I would go with a book like Zettili first. Then you can go on to Ballentine for a more mathy account.

I have heard about Ballentine's book,but its score on amazon is not as good as other hard hitters like Zettili's book.Does Ballentine's text offer as much intuition as mathematical rigor?And if so,how do its mathematics compare to Griffiths and how do they compare with Landau's?

 

[Joker93]

One doesn't need to read all of Landau to benefit from it, just the introductory chapter. There are many good books on quantum mechanics, and starting with an easy one like French and Taylor, or Griffiths is good. Basically, the subject is well-understood, and you should just pick a standard text and check out any others for alternative explanations when you run into difficulty.

Do you know any other good books on par with Landau as far as intuition and maths go?
Also,is there something a bit more advanced than say Griffiths but not as advanced as Landau?

 

[atyy]

Do you know any other good books on par with Landau as far as intuition and maths go?
Also,is there something a bit more advanced than say Griffiths but not as advanced as Landau?

At a level beyond Griffiths, I like Shankar for many nice incidental comments. However, for the formal presentation of quantum mechanical axioms, I like Sakurai and Napolitano and Nielsen and Chuang.

Like Landau and Lifshitz, another valuable book for interpretation is Weinberg (the QM text, not the QFT ones).

 

[micromass]

I have heard about Ballentine's book,but its score on amazon is not as good as other hard hitters like Zettili's book.Does Ballentine's text offer as much intuition as mathematical rigor?And if so,how do its mathematics compare to Griffiths and how do they compare with Landau's?

I don't think amazon score is a very good reference to base your book choice on. Ballentine is not comparable to books like Griffiths and Zettili. It is much more foundational and rigorous. It is also not meant to be an intro book.

 

[atyy]

Also, I should say that I do not consider Ballentine a foundational book from the physics point of view, rather it is one of the most misleading books.

 

[Joker93]

Also, I should say that I do not consider Ballentine a foundational book from the physics point of view, rather it is one of the most misleading books.

What books would you call fundamental?Because i want to own a book that is very fundamental

 

[vanhees71]

I also have Griffith's textbook.Doesn't it offer the same intuition as Landau's textbook?

I don't know Griffith very well, but from discussions in this forum I have the feeling it leads sometimes to unnecessary confusion. Landau/Lifshitz vol. III is a very valuable source to learn QT, but I don't think that it is manageable as a first textbook on a subject. It's also a bit too much overemphasizing the wave-mechanics approach. A modern textbook should use the Hilbert-space formalism.

I'd recommend Sakurai as a first textbook. It was my first textbook at university for QT too, and I loved it (and love it still today) :-).

 

[atyy]

What books would you call fundamental?Because i want to own a book that is very fundamental

My recommendations would be Weinberg or Nielsen and Chuang, but those are closer to the level of Landau and Lifshitz. However, for beginning quantum mechanics I would second vanhees71's recommendation of Sakurai, because it gives a good version Hilbert space formalism pretty close to the start. I would again say the subject can be learned in many ways in starting with French and Taylor and Griffiths is fine, but the Hilbert space formalism, like that given in Sakurai is key to understanding quantum mechanics.

 

[ShayanJ]

Nielsen and Chuang

The only Nielsen and Chuang I know(and was able to find) is "Quantum Computation and Quantum Information"!
Its strange to me you're putting a book on QC and QI with only one chapter on basic QM on equal footing with textbooks written to teach basics of QM!

 

[atyy]

The only Nielsen and Chuang I know(and was able to find) is "Quantum Computation and Quantum Information"!
Its strange to me you're putting a book on QC and QI with only one chapter on basic QM on equal footing with textbooks written to teach basics of QM!

It's one of the few places where the modern Hilbert space formalism is crisply stated. I don't think even Sakurai does it so well. When I was taught quantum mechanics, we got the old version of this in lecture 3 (lecture 1 was dimensional analysis, lecture 2 was black body radiation, lecture 3 was observables, Hilbert space, equation of motion).

The Hilbert space formalism is very important, and since even Sakurai doesn't state it so crisply, here are two other references for it.

Preskill, Lecture Notes on Quantum Computation, http://theory.caltech.edu/people/preskill/ph229/#lecture
The traditional version of the postulates is given as 4 postulates in section 2.1

Paris, The modern tools of quantum mechanics, http://arxiv.org/abs/1110.6815
An modern version of the postulates are given as 5 postulates on p9. For discrete variables, Preskill's and Paris's postulates are equivalent. However, Paris's version generalizes to continuous variables. It is not physically misleading to learn Preskill's version, as the additions needed for continuous variables are mathematical fine points.

 

[A. Neumaier]

I want to learn physics with a lot of intuition but also i want to learn the full mathematics behind each subject.

My online book Classical and Quantum Mechanics via Lie algebras might be the right thing for you, at least as a complement to other texts. In particular, you'll learn from my book nothing about weirdness in quantum mechanics that you'd later need to unlearn again! Your math shouldn't be too poor to be able to follow the text, but several advanced 16 year old's have given me positive feedback.

 

[Joker93]

Guys,thank you all for your recommendations,i will try out the books that you recommended!The truth is that i needed a source that introduced me properly to Hilbert space,so i think that the books that you recommended will be pretty useful as long as there is also physical AND mathematical intuition to back up the plain maths(i am not talking about the solution of a problem for example).

 

[SuperDaniel]

Guys,thank you all for your recommendations,i will try out the books that you recommended!The truth is that i needed a source that introduced me properly to Hilbert space,so i think that the books that you recommended will be pretty useful as long as there is also physical AND mathematical intuition to back up the plain maths(i am not talking about the solution of a problem for example).

Hello Adam,

My very first post in this forum was similar this one... I received almost the same advices you are getting now, and, I can tell that I am using both Landau-Lifshitz as well as Sakurai. Both are excellent, and, despite of I have read in some posts, I haven't found Landau-Lifshitz hard to understand. Even I bought Mechanics and Fluid Mechanics from the same authors.

Good luck

D.

 

[Joker93]

Hello Adam,

My very first post in this forum was similar this one... I received almost the same advices you are getting now, and, I can tell that I am using both Landau-Lifshitz as well as Sakurai. Both are excellent, and, despite of I have read in some posts, I haven't found Landau-Lifshitz hard to understand. Even I bought Mechanics and Fluid Mechanics from the same authors.

Good luck

D.

But didn't the use of advanced mathematics obscure the intuition behind QM?Because,you know,i want it as an introduction to QM.

 

[SuperDaniel]

But didn't the use of advanced mathematics obscure the intuition behind QM?Because,you know,i want it as an introduction to QM.

Well, I have my old calculus books at hand (I took my maths courses during the late 90s). As you well said, calculus can be hard to handle, sometimes... I started to study physics by myself, so, I cannot give you advice, I just can tell you my recent experience studying QM: during these last 6 months, I had to review calculus 1 and 2, as well as Newtonian mechanics. Take it as a challenge.

 

[atyy]

Actually, Landau and Lifshitz are famous for their lack of rigour. They are a bit terse, but first and foremost they are physicists, so they really take care about physical intuition. The mathematics might be advanced, but only in the hand-wavy physics sort of way.

Weinberg is similarly mathematically non-rigourous, but is careful about the physical reasoning.

 

[vanhees71]

But didn't the use of advanced mathematics obscure the intuition behind QM?Because,you know,i want it as an introduction to QM.

The point is that the intuition of QM is mathematics. There's no way to express QM than mathematics, and at the level of physicists' rigor it's not that difficult. My math professor used to say that separable Hilbert spaces are (nearly) as good-natured as finite-dimensional (unitary) vector spaces. This is the more true for the rigged Hilbert spaces that are used by physicists more or less tacitly.