Q.M. Books for Beginners: A 15-Year-Old's Quest

[Gebri Mishtaku]

Hello there peers !
I am an extremely curious fifteen year old boy and I must say that there's nothing more intriguing and superb to get curious about than quantum mechanics. Though don't get the wrong idea that I'm interested in the weirdness of it. Au contraire! Rather I'd consider myself to be "professionally" curious, i.e. I wan't the real deal and am not scared of the mathematics. Instead, I love the way we can communicate with nature in a sensible way through symbols on paper, that's why I entered the beautiful field of physics a few months ago starting to learn calculus and get on going with the overall ideas surrounding our understanding of nature's ways. Now I still have lots to learn in Partial Dequations (PDE) but that's not the point of me making this thread. I would kindly appreciate anyone who can share with me the title of what they consider to be the greatest of books on quantum mechanics, that is both comprehensible by the beginner in Q.M. and also introductory and beyond on the mathematical underlyings of Q.M. I guess you know by now that I love the math of it so no problems from that side. If you think the book is great and does its job well, then I'd be very grateful if you leave a reply below. And by the way you may as well suggest something on partial d's as well while you're on it.
Thank you so much in advance.

 

[jedishrfu]

Welcome to PF!

Assuming you've gotten a good understanding of Classical Mechanics and Electromagnetic theory then the usual recommended one is Griffith's Introduction to QM used as an undergrad book at many colleges:

https://www.amazon.com/dp/0131118927/?tag=pfamazon01-20

One classic would be P.A.M. Diracs treatment:

https://www.amazon.com/dp/0198520115/?tag=pfamazon01-20

 

[bhobba]

Assuming you are not scared of math I would start with Lenny Susskinds books (don't skip the Classical Mechanics one - its very important)
https://www.amazon.com/dp/046502811X/?tag=pfamazon01-20
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20

Those books also have associated video lectures:
http://theoreticalminimum.com/

Then Hughs - The Structure And Interpretation Of QM:
https://www.amazon.com/dp/0674843924/?tag=pfamazon01-20

I would also suggest Griffiths, but it is a bit pricey, so after that I like Quantum Mechanics Dymystified at a more reasonable price:
https://www.amazon.com/dp/B00BPO7APS/?tag=pfamazon01-20

Then you are ready for IMHO simply the best book on QM there is - Ballentine - QM - A Modern Development:
https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20

It is THE book. Once you have mastered that, you are at graduate level in QM.

But don't skip the sequence - each book I have suggested builds on the previous one.

Thanks
Bill

 

[Gebri Mishtaku]

Well, thank you kind people who replied. I'll definitely be picking up Griffiths book as I've heard some pretty good reviews for it and definitely check Leonardo's(inside joke) lectures on youtube.

 

[R136a1]

There are very little physics books which actually do justice to the math in QM. Most books kind of "butcher" it. Of course, this is no problem to me. Physicists are no slaves of mathematicians so they are not forced to do things with a mathematicians' rigor and carefulness. In fact, the mathematicial foundations of QM are so incredibly difficult that it would take a significant time to study all you need. Furthermore, they add not much to the physics, which I assume is what physicists are interested in. Still, you mention being very interested in the math behind QM, so I need to disappoint you and tell you that for a first time learning QM, you're not going to see QM with the right mathematics foundations in your book.

I would recommend you to study some linear algebra first, the book "Linear Algebra done wrong" is freely available and great: www.math.brown.edu/~treil/papers/LADW/book.pdf‎[/URL]
Lang's book is also nice: [URL]https://www.amazon.com/dp/0387962050/?tag=pfamazon01-20[/URL]
Be sure to get well acquainted to dual spaces and inner product, then QM will make waay more sense.

I recommend against Griffiths, I think the book is horrible. I agree with bhobba that Ballentine is probably the best book you can find on QM (and one of the most math-oriented, even though it's not completely rigorous). Then again, Ballentine is a bit advanced. For a first encounter with QM, I think [URL]https://www.amazon.com/dp/0470026790/?tag=pfamazon01-20[/URL] Zettili is your best bet. It's an awesome book with great exercises.

You do know a bit of classical mechanics already, no? If not, you should study that and at least get acquainted with the hamiltonian formalism. The book by Susskind linked by bhobba is great, try to read to that first.

 

[WannabeNewton]

Learn classical mechanics and electromagnetism first.

 

[Jorriss]

Learn classical mechanics and electromagnetism first.

I agree with this, at minimum with respect to classical mechanics. Classical mechanics is still a more appropriate avenue to learn about many mechanical (among other) concepts such as momentum, velocity, kinetic energy, etc which remain central in quantum mechanics.

That being said, if you really want to run with with quantum mechanics then Griffiths and/or Zettili are great choices. Griffiths is very insightful but very basic. Zettili is a tad bit more mature. The main advantage of Zettili is that each chapter has a large selection of worked problems (mostly computational ones - which is good so one can see how one does calculations in quantum mechanics without having to deal with all the tediousness oneself).

 

[George Jones]

I think Zettili's strength is also its weakness:

Zettili is great for seeing how calculations are done, but it is somewhat weak conceptually, and it omits completely some of the most exciting material in modern quantum theory, i.e., quantum entanglement and the EPR paradox and Bell's theorem etc.

 

[Geremia]

One classic would be P.A.M. Diracs treatment:

https://www.amazon.com/dp/0198520115/?tag=pfamazon01-20

Oh, yes! That's probably the greatest physics book of the 20th century.

 

[bhobba]

Oh, yes! That's probably the greatest physics book of the 20th century.

Even though its the book I learned QM from, and the above is true without question, it lags far behind modern treatments like Ballentine in explaining exactly what's going on. For example Ballentine fairly rigorously develops Schrodengers equation from symmetries, Dirac from vague analogies to Poisson Brackets.

Thanks
Bill

 

[bhobba]

In fact, the mathematicial foundations of QM are so incredibly difficult that it would take a significant time to study all you need.

True.

But I hasten to add that anyone with an exposure to Hilbert spaces, which many study undergad, can understand the mathematically rigorous - Mathematical Foundations of QM by Von Neumann.

I just don't want the OP to get the impression a mathematically correct treatment is so difficult its beyond reach.

A note to the OP - until you understand things like Hilbert Spaces it best to stay away from mathematically correct books like Von Neumann

Thanks
Bill

 

[WannabeNewton]

Ballentine doesn't teach you how to do QM. OP, your choice to get Griffiths is probably the best one.

 

[Gebri Mishtaku]

I am understanding something now from reading through all your guys' responses: Learning ways are entirely subjective, thus the many different book suggestions from all of you. It's ok though, I'll go with Griffith's first and see for myself. My favorite way of studying is to hear/read from many perspectives and in the end make up my own, so no problem. Thank you so much everybody :D
And by the way,

I would recommend you to study some linear algebra first...

I have studied linear algebra, vector analysis, state-vector spaces(that's what I call phase spaces) and have developed quite a nice understanding of what the inner product implies physically, not only mathematically. I LOVE VECTORS SO MUCH! And may I say the ket and the bra are the cutest little things in all mathematics?

 

[Gebri Mishtaku]

Oh sorry i forgot to ask: Has anybody gone through "The Road to Reality" by Roger Penrose? If so what did you think of it?

 

[R136a1]

And may I say the ket and the bra are the cutest little things in all mathematics?

I would say they're not part of mathematics to begin with. Only physicists use the notation. Mathematicians tend to hate it

Oh sorry i forgot to ask: Has anybody gone through "The Road to Reality" by Roger Penrose? If so what did you think of it?

It's more of a popsci book (a very very rigorous popsci book). It's a nice book to give you some intuition on the subject, but it's not good at all to use it to learn physics and math properly.

 

[jedishrfu]

Oh sorry i forgot to ask: Has anybody gone through "The Road to Reality" by Roger Penrose? If so what did you think of it?

My feeling is it will be overwhelming of the casual reader but for a recent undergrad physics major they would be able to plow through it without too much difficulty.

 

[Gebri Mishtaku]

I would say they're not part of mathematics to begin with. Only physicists use the notation. Mathematicians tend to hate it
It's more of a popsci book (a very very rigorous popsci book). It's a nice book to give you some intuition on the subject, but it's not good at all to use it to learn physics and math properly.

The ket and the bra are definitely mathematical symbols used in a mathematical way. To say they don't belong in mathematics is kind of not the smartest thing because everything you can do with them falls into the realm of math. Except a very interesting idea I have of a t-shirt but not now...
And I couldn't agree more on the book. It feels very ambiguous when you go through it, just doesn't feel right. Probably because it was made for the public, but it throws math down the readers' throat in every page. My mistake I bought it thinking of it as a rigorous book.

 

[R136a1]

The ket and the bra are definitely mathematical symbols used in a mathematical way. To say they don't belong in mathematics is kind of not the smartest thing because everything you can do with them falls into the realm of math. Except a very interesting idea I have of a t-shirt but not now...

I'm just saying that mathematicians very rarely use braket notation and prefer other notations which they find easier. Physicists prefer braket notations over the mathematician's notations. If you read a math book, then you will almost never encounter braket notation, you'll only see it in physics books or papers. So in that way, they are more about physics than about math.

Not saying that a good mathematician shouldn't use braket notation. But it turns out that few actually use it consistently for some reason.

 

[Gebri Mishtaku]

I wasn't arguing about whether mathematicians use brackets or not I was just saying that the bra ket notation is mathematical, otherwise we wouldn't use it to describe nature.

 

[WannabeNewton]

I wasn't arguing about whether mathematicians use brackets or not I was just saying that the bra ket notation is mathematical, otherwise we wouldn't use it to describe nature.

http://arxiv.org/pdf/quant-ph/9907069.pdf

Anyways, this is getting off-topic. Check out Griffiths and see how much you like it. Good luck!

 

[R136a1]

I wasn't arguing about whether mathematicians use brackets or not I was just saying that the bra ket notation is mathematical, otherwise we wouldn't use it to describe nature.

Mathematics doesn't really care about describing nature.

Anyway, we seem to have a quite definition of "mathematical". And if two people don't accept the same definitions, then they can never agree. So we'll have to agree to disagree.

Let's just say that if you like braket notation and are comfortable using it, then you should obviously keep on using it.

 

[Gebri Mishtaku]

We use it to describe the patterns we see around us though, don't we? Anyways, thank you for your time and keep mathin!

 

[bhobba]

Oh sorry i forgot to ask: Has anybody gone through "The Road to Reality" by Roger Penrose? If so what did you think of it?

Yes - gone through it.

Its rather unique in what it sets out to do and well worth reading.

But be aware, while a majestic achievement by any measure, and I sit in awe of Roger's accomplishment in writing it, judged from the very highest levels of scholarship it does have a few issues as you will find from a couple of reviews.

Thanks
Bill

 

[bhobba]

I would say they're not part of mathematics to begin with. Only physicists use the notation. Mathematicians tend to hate it

Hmmmm.

Not so sure about that.

I tend to be more interested in physics, especially quantum physics, these days, but in times gone by I was rather interested in Stochastic modelling. The whole area of Hida distributions as found in say Stochastic Partial Differential Equations by Birkhauser uses it quite a bit - but that area makes extensive use of Rigged Hilbert spaces for which that notation is very natural.

IMHO it purely depends on what area of math it is.

Thanks
Bill

 

[R136a1]

Hmmmm.

Not so sure about that.

I tend to be more interested in physics, especially quantum physics, these days, but in times gone by I was rather interested in Stochastic modelling. The whole area of Hida distributions as found in say Stochastic Partial Differential Equations by Birkhauser uses it quite a bit - but that area makes extensive use of Rigged Hilbert spaces for which that notation is very natural.

IMHO it purely depends on what area of math it is.

Thanks
Bill

Well, braket notation really makes way more sense in rigged Hilbert spaces, and the alternatives tend to be ugly there.

But my point was that of course you'll find some mathematicians who use the braket notation. However, the majority of people working in functional analysis and the like, don't use the notation. Likewise, the majority of physicists do use the notation. Of course you'll find some physicists hating the notation and some mathematicians loving the notation. But that's not my point.

 

[bhobba]

But my point was that of course you'll find some mathematicians who use the braket notation. However, the majority of people working in functional analysis and the like, don't use the notation. Likewise, the majority of physicists do use the notation. Of course you'll find some physicists hating the notation and some mathematicians loving the notation. But that's not my point.

I certainly agree with that.

I would say they're not part of mathematics to begin with. Only physicists use the notation. Mathematicians tend to hate it

It was just, before clarifying it, what you said above wasn't really reflective, to my mind anyway, of what's going on. I think both camps choose the notation most convenient for their purposes. The true basis of the math of QM is Rigged Hilbert Spaces, although physicists only occasionally admit to it, saying what they deal with is Hilbert spaces. That's why they use the bra-ket notation, because as you correctly point out the usual notation doesn't really work well there.

However physicists are not the only ones into Rigged Hilbert spaces, and some areas of math, such as Hida Distributions, find their natural expression in that formalism, and its used there as well. Really its horses for courses, not that mathematicians hate it etc.

I have to say my background is math and not physics, and I originally resisted the bra-ket notation, but found in QM it offered so many advantages I eventually conformed. Now when I return to linear algebra or functional analysis I find the opposite - I use the bra-ket notation - habits one way or the other are hard to break, but once broken, equally hard to reestablish. It just seems to be the nature of things.

Thanks
Bill

 

[WannabeNewton]

I have to say my background is math and not physics, and I originally resisted the bra-ket notation, but found in QM it offered so many advantages I eventually conformed. Now when I return to linear algebra or functional analysis I find the opposite - I use the bra- ket notation - habits one way or the other are hard to break, but once broken, equally hard to reestablish. It just seems to be the nature of things.

Boy can I relate! You should see how much I struggle with the notation in proper differential geometry texts: I'm so used to abstract index notation and Einstein summation that it's second nature to me now and impossible for me to refrain from using it when working through a proper differential geometry text. It's perfectly understandable why physicists elatedly prefer to use notation schemes like braket notation and abstract index notation because they have an unequivocally superior calculational prowess that the respective mathematics notation schemes lack.