I'm looking for a Quantum Mechanics textbook

[anachin6000]

The title kind of says it all, but I'm searching for a textbook that has a heavy theoretical approach. Could someone help me with a recommendation?

 

[PeroK]

The title kind of says it all, but I'm searching for a textbook that has a heavy theoretical approach. Could someone help me with a recommendation?

Is this a first textbook or advanced?

 

[anachin6000]

Is this a first textbook or advanced?

First.

 

[PeroK]

First.

Try doing a search on here. I like Griffiths and Sakurai (in that order), but there are lots of other recommendations for the likes of Townsend and McIntyre:

https://www.physicsforums.com/threads/griffiths-or-zettili.896548/#post-5639700

https://www.physicsforums.com/threads/quantum-mechanics-townsend-or-mcintyre.888655/#post-5589884

 

[dextercioby]

JJ Sakurai's book is brilliant (well, I don't like his lack of mathematical rigor, but that's just me), but not as a first text/exposure to the interesting world of quantum physics.

 

[atyy]

For a first book, philosophy is more important than theory, so I recommend Landau and Lifshitz. Weinberg is also good.

 

[vanhees71]

For a first book philosophy is confusing (it's confusing even for the advanced physicist) and not very helpful concerning the understanding of the hard facts about QT. I don't understand, how you can recommend Landau and Lifshitz and Weinberg with the argument "philsophy is more important than theory"! I'd recommend these very books for the opposite reason. They do not contain unnecessary philosophical gibberish but follow a "no-nonsense approach". I like Landau and Lifshitz, but for my taste it's too much "wave-mechanics centered" in its approach rather than starting in the very beginning with the Dirac approach, which makes the underlying logic of QT much more explicit than using a specific representation (i.e., the position representation). I'd however not recommend Weinberg as a first read, because it's pretty advance (but of course brilliant as any textbook by Weinberg). If I had to teach QM1, I'd still recommend J. J. Sakurai's book, from which I learned QT as a student in my QM1 lecture.

 

[Demystifier]

By "philosophy", I believe that atty means an emphasis on concepts rather than techniques of calculation. In that sense, I would agree that concepts are more important than techniques in a first exposition to QM.

 

[dextercioby]

In other words (4), more text, less formulas.

 

[Demystifier]

In other words (4), more text, less formulas.

Sort of, but it's also important that most formulas are short so that one can comprehend their conceptual meaning at a single glance. An example would be the equation for the Green function written as
$$LG=1$$
where ##L## is a differential operator. But then again, perhaps this particular equation is too abstract for a first exposition, so one has to explain in a longer formula what such compact notation really means.

 

[smodak]

The title kind of says it all, but I'm searching for a textbook that has a heavy theoretical approach. Could someone help me with a recommendation?

A good theoretical book on Quantum Mechanics is Gottfried https://www.amazon.com/dp/0387220232/?tag=pfamazon01-20
But I do not think you should start with that book.
Start With McIntyre (it is better to understand the concepts first) https://www.amazon.com/dp/0321765796/?tag=pfamazon01-20 along with Bowman https://www.amazon.com/dp/0199228930/?tag=pfamazon01-20

Then read Gottfried (https://www.amazon.com/dp/0387220232/?tag=pfamazon01-20 ) and possibly also Ballentine (https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20)

By the way, if you provided us a little bit of your background, your current knowledge of math and physics, and why you want a book, it would have been easier for us to recommend what may be most appropriate for you.

 

[vanhees71]

In other words (4), more text, less formulas.

Hm, I hate textbooks with a suada of words like "as one easily sees, the following theory of everything is valid" instead of writing the one or other formula to derive it! Take Sommerfeld's 6-volume lecture series: Many formulae with the right amount of words. The result is a didactic master piece. If you look at the list of his pupils, it should be proof enough that this is the way theoretical physics should be taught!

 

[Andreol263]

Griffiths is terrible, it's just a minor step up from basic introductory modern physics texts, and it appears to be allergic to dirac notation.
I Would recommend Shankar's Principles of Quantum Mechanics, for it being extremely well self-contained and very didatic and fun to learn from, and the exercises are in the right spot :D

 

[atyy]

For a first book philosophy is confusing (it's confusing even for the advanced physicist) and not very helpful concerning the understanding of the hard facts about QT. I don't understand, how you can recommend Landau and Lifshitz and Weinberg with the argument "philsophy is more important than theory"! I'd recommend these very books for the opposite reason. They do not contain unnecessary philosophical gibberish but follow a "no-nonsense approach". I like Landau and Lifshitz, but for my taste it's too much "wave-mechanics centered" in its approach rather than starting in the very beginning with the Dirac approach, which makes the underlying logic of QT much more explicit than using a specific representation (i.e., the position representation). I'd however not recommend Weinberg as a first read, because it's pretty advance (but of course brilliant as any textbook by Weinberg). If I had to teach QM1, I'd still recommend J. J. Sakurai's book, from which I learned QT as a student in my QM1 lecture.

Yes, ideally we should combined the philosophy of Landau and Lifshitz or Weinberg with the the Sakurai starting with spin 1/2. I like the calculation part of Sakurai, unfortunately he doesn't do philosophy that well, so I still recommend L&L or Weinberg for that.

 

[vanhees71]

Hm, I don't find much "philosophy" in either of these books; perhaps most is in Weinberg's about "interpretation".

 

[atyy]

Hm, I don't find much "philosophy" in either of these books; perhaps most is in Weinberg's about "interpretation".

Well, the typical L&L is to do the minimum but clearest of everything :)

 

[vanhees71]

Yes, concerning "representation" L&L is very good, at least there's no collapse ;-).

 

[atyy]

Yes, concerning "representation" L&L is very good, at least there's no collapse ;-).

L&L have collapse :)

Actually their collapse part is a bit old fashioned, but it's still much better than having no collapse.

 

[Demystifier]

Yes, concerning "representation" L&L is very good, at least there's no collapse ;-).

L&L have collapse :)

Oh no, not again!

L&L do not use the word "collapse", but they certainly do introduce a non-unitary process. At page 24 they say (my bolding):
"We see that the measuring process in quantum mechanics has a "two-faced" character: it plays different parts with respect to the past and future of the electron. With respect to the past, it "verifies" the probabilities of the various possible results predicted from the state brought about by the previous measurement. With respect to the future, it brings about a new state (see also §44). Thus the very nature of the process of measurement involves a far-reaching principle of irreversibility.This irreversibility is of fundamental significance. We shall see later (at the end of §18) that the basic equations of quantum mechanics are in themselves symmetrical with respect to a change in the sign of the time; here quantum mechanics does not differ from classical mechanics. The irreversibility of the process of measurement, however, causes the two directions of time to be physically non-equivalent, i.e. creates a difference between the future and the past."

Clearly, irreversibility implies non-unitarity. It is a matter of interpretation and semantics to explain whether this non-unitarity is or isn't the same as collapse. But it seems to me that for L&L this non-unitarity is a physical process, and not merely an update of information. So it would be really illuminating if vanhees could clarify how exactly this L&L's irreversible physical process can be different from collapse.

 

[Demystifier]

Hm, I hate textbooks with a suada of words like "as one easily sees, the following theory of everything is valid" instead of writing the one or other formula to derive it! Take Sommerfeld's 6-volume lecture series: Many formulae with the right amount of words. The result is a didactic master piece. If you look at the list of his pupils, it should be proof enough that this is the way theoretical physics should be taught!

Yes, but physics is not only theoretical physics. A first book on a topic such as QM should be understandable to all physicists.

 

[Vanadium 50]

There are things I like about Landau and Lifshitz, but unfortunately those are the same things that make me not recommend it for beginners. ("The natural choice of coordinates for the hydrogen atom is parabolic")

I prefer Liboff to Griffiths. He starts out with necessary background. The complaint that Griffiths is to differential equation-y and not matrix-y enough could apply to Liboff as well, but not to the same degree.

 

[mpresic]

I have taken graduate courses in QM at 4 different Universities and undergraduate course in QM in 1 University. I have noted one common characteristic.

Faculty in all 5 universities mentioned they had trouble finding a good textbook to fit their entire needs. All but one used Sakurai, for graduate level QM, but assigned some though not all problems out of Sakurai. The faculty reserved some homework problems that they created and assigned.

All of the faculty taught from their own note (that is part of what we pay them for) , which is harder than using a textbook. You can find graduate QM notes on the internet for Illinois, Colorado, and San Diego taught by faculty. These are all good schools. (Take your pick).

I found other faculty in classical mechanics also taught from notes, but these notes bore a much stronger resemblance to the textbook (typically Goldstein, Classical Mechanics) than in the graduate level QM courses.

For a first course, I recommend older texts like Merzbacher (quite advanced undergraduate and graduate level). Sakurai admits in the foreward, preface, or somewhere in the book he leaves out material, he expects the reader to get in an earlier course.

Shankar is complete but I regard this as advanced too.

I like Messiah, and it is out in inexpensive Dover. As a first year grad student before Sakurai, I switched learning relevant sections from three textbooks, Schiff, Powell and Crasemann, and Messiah.

I do not criticize (as some do) that some texts are wave-mechanics oriented. I think this may be more natural to some (e.g. chemists) than the abstract Dirac notation approach, especially in an introductory course.

 

[Demystifier]

I do not criticize (as some do) that some texts are wave-mechanics oriented. I think this may be more natural to some (e.g. chemists) than the abstract Dirac notation approach, especially in an introductory course.

Wave mechanics is also useful in order to understand that quantum mechanics is a modification of classical mechanics, and not something completely different from everything else what one learned about physics before.

 

[smodak]

Cannot say for others, but I did find learning through Dirac notation much easier than the wave mechanics. I find the spins -first approach (used by Sakurai, Townsend, McIntyre etc.) using Dirac notation from the get go the easiest (and some would argue most modern way) to learn quantum mechanics.

 

[Demystifier]

So there are at least two types of QM textbooks:
1. wave function first
2. spin first

Are there any others? A path-integral first perhaps?

 

[PeroK]

Cannot say for others, but I did find learning through Dirac notation much easier than the wave mechanics. I find the spins -first approach (used by Sakurai, Townsend, McIntyre etc.) using Dirac notation from the get go the easiest (and some would argue most modern way) to learn quantum mechanics.

The advantage for me of not learning Dirac notation immediately was that it was one less thing to worry about. I could rely on my knowledge of linear algebra, very much as an anchor. Learning Dirac notation was not initially essential and could wait.

It also seems to me from questions in this forum that many students rely on Dirac as some sort of algebraic magic, without much understanding of the linear algebra that underpins it.

 

[smodak]

So there are at least two types of QM textbooks:
1. wave function first
2. spin first

Are there any others? A path-integral first perhaps?

I would not put it quite that way. I think there are two basic approaches

1. Spins First
2. Traditional (sort of Historical)

Spins first approach, by default, starts with Dirac Notation before moving on to Wave Mechanics.
The traditional approach can live anywhere in the spectrum of using state vectors and Dirac Notation from the get go or even avoid them mostly.

 

[smodak]

The advantage for me of not learning Dirac notation immediately was that it was one less thing to worry about. I could rely on my knowledge of linear algebra, very much as an anchor. Learning Dirac notation was not initially essential and could wait.

It also seems to me from questions in this forum that many students rely on Dirac as some sort of algebraic magic, without much understanding of the linear algebra that underpins it.

Well, the assumption is that we know basic linear algebra before starting to learn Quantum mechanics - Dirac notation is 'syntactic sugar' - a very sweet one for me :) As I said, it really worked for me but every one learns differently and there is no panacea.

I have not seen the spins first approach done without using state vectors and Dirac notations (bras and kets) - II guess it may be possible. The spins first approach is my favorite approach. So, by definition my approach leans on Dirac Notation.

 

[Vanadium 50]

Are there any others?

Commutators first.

 

[atyy]

A book that is introductory but takes the formalism first appproach is Le Bellac's Quantum Physics.[URL='https://www.amazon.com/dp/0521852773/?tag=pfamazon01-20
[/URL]
https://www.amazon.com/dp/0521852773/?tag=pfamazon01-20

It is in the terrific French tradition (Messiah, Cohen-Tannoudji).

Although the modern French get the philosophy right, they state it too subtly, so I would still recommend Landau and Lifshitz along with any first quantum textbook.

 

[Demystifier]

Commutators first.

Some good examples?

 

[Vanadium 50]

I don't know of any books that do it this way. I have some decades-only lecture notes. (You asked for approaches, not instances.)

It's not necessarily stupid, although I think it would have worked better had I been solid with Poisson brackets.

 

[atyy]

Some good examples?

Maybe https://books.google.com.sg/books?id=Bn7MaT3X8fkC&source=gbs_navlinks_s

In a way also https://www.amazon.com/dp/0470026790/?tag=pfamazon01-20 which mentions the uncertainty principle in chapter 1, and then derives the uncertainty principle from commutation relations in chapter 2.

Of course it's a bit unfortunate that Heisenberg's historical argument doesn't have that much to do with the usual uncertainty principle, and many textbooks motivate the latter from the former.

 

[dextercioby]

I would take out the Heisenberg microscope and the sound wave analogy from any textbook.

 

[atyy]

I would take out the Heisenberg microscope and the sound wave analogy from any textbook.

Or keep it and add the correct dervation of the Heisenberg microscope from the commutation relations.