Best way to learn QM comprehensively

[dustytretch]

I want to go about learning quantum mechanics in a way that I can learn it in detail eventually.
And I was wondering if someone could give me some advice or advice for how they learn't it,
should I start learning calculus and the mathematics needed for understanding
it or get one of these books that were recommended on a thread on this forum such as
introduction to quantum mechanics by Griffiths or quantum reality: theory and philosophy by Allday.
Any pointers?
The main question is, learn the mathematics first or get a book that will cover it in it?

 

[nonequilibrium]

It depends on your current mathematical knowledge; if you don't know calculus yet, then definitely get the hang of that first. It would help if you specify your math knowledge so far.

 

[dustytretch]

It depends on your current mathematical knowledge; if you don't know calculus yet, then definitely get the hang of that first. It would help if you specify your math knowledge so far.

I am at the end of my maths GCSE, so I only know very basic trigonometry, quadratics.
Thats about it.

 

[QuarkCharmer]

You need the mathematics before you even attempt it. Unless you are just interested in reading popular interpretations and such.

 

[saim_]

Take further maths in A-level. After school, it gave me enough to start working at a snail's pace on a QM text, but, of course, even all the further math stuff soon runs out in a QM text and you will need good courses in multivariable calculus, linear algebra and differential equations to get a good grip on most of the stuff.

 

[spaghetti3451]

I am at the end of my maths GCSE, so I only know very basic trigonometry, quadratics.
Thats about it.

Don't even think about attempting to understand QM in all its rigour. When I read your first post, I thought you were a first-year undergrad, but now given your background I'd say there's only a one in a million chance that you will even understand half of QM properly given your mathematical background.

Students take years to familiarise themselves with linear algebra, differential equations, vector calculus and multivariable calculus. It cannot be done in a few weeks. It will take at least a couple of months. And then you will need to have a sufficient bakcground of classical mechanics because the standard way to introduce QM to students is through their understanding of classical mechanics. You can of course find resources that do not use this approach, but no matter what textbook, the authors assume that the student is an undergrad and they use reasonably complicated and perplexing terminology and generalisations, so it can get confusing.

That's unless you just want a general picture of QM, which is perfectly possible given your level of mathematical background.

 

[twofish-quant]

Don't even think about attempting to understand QM in all its rigour.

Don't even think about this because I don't think that anyone really understands QM.

Most undergraduate courses focus on giving you enough understanding of QM so that you can solve practical problems. That will take you about two to three years from where you are.

One book I recommend is the classic French and Taylor. The reason I like it is that it's a stepping stone between "popular" accounts of QM and the "deep mathematical" parts.

 

[dustytretch]

Don't even think about this because I don't think that anyone really understands QM.

Most undergraduate courses focus on giving you enough understanding of QM so that you can solve practical problems. That will take you about two to three years from where you are.

One book I recommend is the classic French and Taylor. The reason I like it is that it's a stepping stone between "popular" accounts of QM and the "deep mathematical" parts.

That is the sort of book I was looking for, how does it compare to something
like griffiths, or are they for different sorts of purposes?

 

[twofish-quant]

That is the sort of book I was looking for, how does it compare to something
like griffiths, or are they for different sorts of purposes?

It's more basic than Griffiths. Some people think "too easy" but it's something that's a stepping stone to Griffiths.

Also

http://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2006/

 

[dustytretch]

It's more basic than Griffiths. Some people think "too easy" but it's something that's a stepping stone to Griffiths.

Also

(I had to remove the link due to my post count)

Thanks for the help, I will get on with ordering it from amazon!

 

[dustytretch]

I suppose this does beg the question, at my level is it possible to teach myself QM beyond popular interpretations?

 

[Fredrik]

I suppose this does beg the question, at my level is it possible to teach myself QM beyond popular interpretations?

It's possible, but it won't be easy.

 

[dustytretch]

It's possible, but it won't be easy.

I suppose though if I do learn these sort of things now, it *should* make things easier later on, or it will just cause me to fail my GCSEs and A-levels

 

[Mépris]

I suppose though if I do learn these sort of things now, it *should* make things easier later on, or it will just cause me to fail my GCSEs and A-levels

MIT's 18.01 course *seems* to cover all the calculus parts of C1-C4 in the A-Level maths syllabus. You could start off with that and move your way up. Learn the chapters that come before calculus from your A-Level textbook and then use 18.01 from OCW. I'd have done just that, had I known about OCW then! When you finish, 18.01, do 18.02 and then start doing some physics from 8.01 and 8.02. Actually, you might be able to start right after 18.01. Also, 8.01 might help you for your mechanics modules.

Note that I haven't actually checked the syllabus word-for-word and it seemed to closely match what I did with CIE (my A-Level board) all the way up to differential equations. The above is more for your own personal study (suggested course of action - I may be wrong/you can disagree with me) and should not replace what you do in your A-Level classes at school! Focus on doing well on those, for you will need excellent grades (although A*AA-AAB will be fine, depending on where you're applying) to get into a good physics undergrad program in the UK.

 

[dustytretch]

MIT's 18.01 course *seems* to cover all the calculus parts of C1-C4 in the A-Level maths syllabus. You could start off with that and move your way up. Learn the chapters that come before calculus from your A-Level textbook and then use 18.01 from OCW. I'd have done just that, had I known about OCW then! When you finish, 18.01, do 18.02 and then start doing some physics from 8.01 and 8.02. Actually, you might be able to start right after 18.01. Also, 8.01 might help you for your mechanics modules.

Note that I haven't actually checked the syllabus word-for-word and it seemed to closely match what I did with CIE (my A-Level board) all the way up to differential equations. The above is more for your own personal study (suggested course of action - I may be wrong/you can disagree with me) and should not replace what you do in your A-Level classes at school! Focus on doing well on those, for you will need excellent grades (although A*AA-AAB will be fine, depending on where you're applying) to get into a good physics undergrad program in the UK.

I have not started maths A-level yet, that will be at the end of 2013 when I start it as I am in year 10 now.
In year 11 I am doing a AQA FSMQ, which is mean't to be a bridge to A level maths.

 

[Mépris]

I have not started maths A-level yet, that will be at the end of 2013 when I start it as I am in year 10 now.
In year 11 I am doing a AQA FSMQ, which is mean't to be a bridge to A level maths.

Well, you'll have to go through A-Level maths, or part of it at least, before you're able to learn some physics. A-Level physics is just algebra based stuff...

Hmm. I believe I did something similar when I did O-Levels - it was called "Additional Mathematics" and covered most of C1-C2. (or P1 for CIE)

 

[genericusrnme]

Do not touch griffiths.
EVER

Step 1. Maths - M Boas, Mathematical Methods in the Physical Sciences, learn the calculus in that book
Step 2. Check out Landau and Lifgarbagez non relitivistic QM book (the first third of it at least)

You'll know where to go from there!

Good luck OP

 

[dustytretch]

Do not touch griffiths.
EVER

Step 1. Maths - M Boas, Mathematical Methods in the Physical Sciences, learn the calculus in that book
Step 2. Check out Landau and Lifgarbagez non relitivistic QM book (the first third of it at least)

You'll know where to go from there!

Good luck OP

This is what I was looking for, you have made my day.
I will get on with ordering that maths book!

 

[saim_]

Do not touch griffiths.
EVER

Step 1. Maths - M Boas, Mathematical Methods in the Physical Sciences, learn the calculus in that book
Step 2. Check out Landau and Lifgarbagez non relitivistic QM book (the first third of it at least)

You'll know where to go from there!

Good luck OP

I strongly disagree with this advice. Boas presumes university level calculus 1, or at least maturity at that level, and Landau doesn't have the 'fun' and explanatory prose that Griffiths has, and, it's more formal. I did first three chapters of Griffiths in high school and I don't think I could have put up with any other QM text for long back then. For a good basic understanding, all it requires is A-level calculus and a good chapter on vector spaces from an "additional math" kind of high-school book. Whereas both Boas and Landau are gems, I think they are inappropriate for a school kid; post freshman year at university, they are your friends.

 

[genericusrnme]

I strongly disagree with this advice. Boas presumes university level calculus 1, or at least maturity at that level, and Landau doesn't have the 'fun' and explanatory prose that Griffiths has, and, it's more formal. I did first three chapters of Griffiths in high school and I don't think I could have put up with any other QM text for long back then. For a good basic understanding, all it requires is A-level calculus and a good chapter on vector spaces from an "additional math" kind of high-school book. Whereas both Boas and Landau are gems, I think they are inappropriate for a school kid; post freshman year at university, they are your friends.

I wouldn't say university level calculus, there's no prerequisite for Boas that you couldn't lean via say Khan Academy in a few days.
L&L certainly don't have a traditional 'fun' but there's certainly an unconventional fun in there and I'd say their explanations are better than Griffiths', especially when relating to the mathematical side of things (especially ladder operators, Griffiths mangles the whole concept into something only understandable if you learn about it somewhere else then completely ignore anything Griffiths has to say about them imo). I do agree that Boas and L&L may be hard for him but if he puts effort into it and does the problems he'll have no problem with it.

 

[dustytretch]

I strongly disagree with this advice. Boas presumes university level calculus 1, or at least maturity at that level, and Landau doesn't have the 'fun' and explanatory prose that Griffiths has, and, it's more formal. I did first three chapters of Griffiths in high school and I don't think I could have put up with any other QM text for long back then. For a good basic understanding, all it requires is A-level calculus and a good chapter on vector spaces from an "additional math" kind of high-school book. Whereas both Boas and Landau are gems, I think they are inappropriate for a school kid; post freshman year at university, they are your friends.

I was wondering about that, as I have only heard good things about Griffiths.

 

[genericusrnme]

I was wondering about that, as I have only heard good things about Griffiths.

https://www.physicsforums.com/showthread.php?t=259974

 

[dustytretch]

https://www.physicsforums.com/showthread.php?t=259974

I was wrong

 

[saim_]

I wouldn't say university level calculus, there's no prerequisite for Boas that you couldn't lean via say Khan Academy in a few days.

You are right, but, remember this is not so for someone who has yet to learn to prove simple trigonometric identities and finding planes given vectors :) There is a reason why all this that seems so simple to us now, we also spent two whole years learning in A-level. You don't get the maturity and the grasp to build on these things if you learn them in a few days.

...I'd say their explanations are better than Griffiths', especially when relating to the mathematical side of things

I think that is indisputably true, but, it is so because they expect more background from the reader.

 

[genericusrnme]

You are right, but, remember this is not so for someone who has yet to learn to prove simple trigonometric identities and finding planes given vectors :) There is a reason why all this that seems so simple to us now, we also spent two whole years learning in A-level. You don't get the maturity and the grasp to build on these things if you learn them in a few days.

Regardless of how long the standard syllabus should last I firmly believe that you could learn the prerequisites for Boas very quickly, certainly in less than a year, I'd be willing to bet less than a month.

You need
1. know what differentiation and integration are
1 day to a week on khan academy
2. basic vector stuff
a week on khan academt (or a week with Gilbert Strang's Introduction to Linear Algebra)

and you're ready to go!
all kitted up in ~a fortnight

As an example that this is possible, this is pretty much the route I took to learning. I dropped out of high school and studied in this way I then applied to sit my exams and got an A in maths. I did this starting of with only GCSE equivelant math knowledge. Just takes a little determination and a lot of work!

I believe OP could achive this, as I did, if he works hard enough at it

 

[saim_]

I believe OP could achive this, as I did, if he works hard enough at it

Can't argue with that :D

 

[dextercioby]

Can one explain to me why in the US such a delicate subject as QM is taught in 2 ways: to undergraduates and to graduates ? What's the difference and why is it a need to teach in 2 different ways ? A serious course should not be taught unless some specific knowledge is already present in the student's head.

To answer the OP, in my humble opinion, to learn QM comprehensively means to adopt the following path for physics & mathematics:

- Classical mechanics with a course based on Goldstein (+ Landau).
- Classical electromagnetism and special relativity with a course based on J.D. Jackson (+ Landau).
- Mathematics courses on linear algebra, abstract algebra, multivariate calculus, ODE's + PDE's, complex analysis and Fourier calculus, functional analysis and group (representation) theory (including Lie algebras).

With this whole package, one's ready for a serious QM book, like Galindo & Pascual (2 volumes).
Having learned QM comprehensively, the student can go for General Relativity based on Wald's book and formal QFT inspired from Weinberg's 3 volumes.

 

[saim_]

Can one explain to me why in the US such a delicate subject as QM is taught in 2 ways: to undergraduates and to graduates ? What's the difference and why is it a need to teach in 2 different ways ? A serious course should not be taught unless some specific knowledge is already present in the student's head.

To answer the OP, in my humble opinion, to learn QM comprehensively means to adopt the following path for physics & mathematics:

- Classical mechanics with a course based on Goldstein (+ Landau).
- Classical electromagnetism and special relativity with a course based on J.D. Jackson (+ Landau).
- Mathematics courses on linear algebra, abstract algebra, multivariate calculus, complex analysis and Fourier calculus, functional analysis and group (representation) theory (including Lie algebras).

With this whole package, one's ready for a serious QM book, like Galindo & Pascual (2 volumes).
Having learned QM comprehensively, the student can go for General Relativity based on Wald's book and formal QFT inspired from Weinberg's 3 volumes.

How about learning addition with real number axioms in kindergarten? :p

 

[Mépris]

Regardless of how long the standard syllabus should last I firmly believe that you could learn the prerequisites for Boas very quickly, certainly in less than a year, I'd be willing to bet less than a month.

You need
1. know what differentiation and integration are
1 day to a week on khan academy
2. basic vector stuff
a week on khan academt (or a week with Gilbert Strang's Introduction to Linear Algebra)

and you're ready to go!
all kitted up in ~a fortnight

As an example that this is possible, this is pretty much the route I took to learning. I dropped out of high school and studied in this way I then applied to sit my exams and got an A in maths. I did this starting of with only GCSE equivelant math knowledge. Just takes a little determination and a lot of work!

I believe OP could achive this, as I did, if he works hard enough at it

Yes, that can be done. The A-Level math syllabus is not one that's too hard and for someone with the determination (and let's assume they can already do basic math well enough), the whole syllabus could be studied within 5-6 months. (including the "applied" components) As far as just "getting an A" on the exam goes, I don't have a problem with that.

I don't think it's a particularly good idea to move so quickly with the calculus, though. I may be wrong, seeing as I've only (nearly) just finished A-Levels myself but I find that there are *many* gaps in how the subjects are presented. For instance, one can finish the course with an A* and barely have an idea of what a limit of a function is or what a Taylor Series is. Things like that are covered in a good Calc I course, it would seem.

 

[twofish-quant]

Can one explain to me why in the US such a delicate subject as QM is taught in 2 ways: to undergraduates and to graduates ?

Because the goals are different.

The purpose of an undergraduate QM class is to teach enough of the topic to undergraduates so that the can do "industrial calculations." There are large industries (semiconductors) that require people to be able to do calcuations in QM and undergraduate classes are geared toward teaching people how to do those calculations.

The purpose of a graduate QM class is to teach the parts of QM that are necessary to do research. This happens at a different energy scale than undergraduate QM and the goals and the methodology are different. Most of what is taught in graduate QM is not "industrially useful."

 

[twofish-quant]

Also, it's useful to get different textbooks, because different people will explain the same things in different ways, and having different explanations will help you see what is going on. If one textbook doesn't make sense, then find the explanation in textbook B, and then once you understand that, then reread textbook A.

 

[Fredrik]

Can one explain to me why in the US such a delicate subject as QM is taught in 2 ways: to undergraduates and to graduates ? What's the difference and why is it a need to teach in 2 different ways ? A serious course should not be taught unless some specific knowledge is already present in the student's head.

To answer the OP, in my humble opinion, to learn QM comprehensively means to adopt the following path for physics & mathematics:

- Classical mechanics with a course based on Goldstein (+ Landau).
- Classical electromagnetism and special relativity with a course based on J.D. Jackson (+ Landau).
- Mathematics courses on linear algebra, abstract algebra, multivariate calculus, ODE's + PDE's, complex analysis and Fourier calculus, functional analysis and group (representation) theory (including Lie algebras).

With this whole package, one's ready for a serious QM book, like Galindo & Pascual (2 volumes).
Having learned QM comprehensively, the student can go for General Relativity based on Wald's book and formal QFT inspired from Weinberg's 3 volumes.

I disagree with some of this. I dislike Goldstein's book more than anything else in physics. I hate the notation, his explanations, and even the smell of the second edition. There is however a third, so maybe it doesn't have to smell bad. Landau & Lifgarbagez looks good to me, but I haven't actually studied it. It should be mentioned that it's a short book that explains how to solve a wide range of problems in classical mechanics. This makes me think that it's a great choice for people who already understand the foundations of the theory and want to get better at doing problems, but not such a great choice who people who just want to understand the foundations of the theory and to be able to solve simple problems. I don't really have any recommendations of my own. I guess V.I. Arnold for the math nerds, but for typical physics students...I just don't know. Maybe L & L is the way to go.

I'm also not a fan of Jackson. It's an absurdly difficult book, and the payoff isn't good enough to justify the effort. At least not for future theorists and teachers. But maybe it is for future engineers and experimentalists. The reason I say this is that it's a book about how to solve every conceivable type of problem, but it doesn't explain the foundations very clearly. At least that's how I remember it, but it's been a long time since I was forced to study it. I don't know what to recommend for classical electrodynamics, but I've seen recommendations in other threads, so if I had been thinking about buying a book on this topic, I'd search for recommendations in the book forum.

I don't know enough about Galindo & Pascual to comment on that recommendation. I'll just say that for QM, I think Griffiths looks adequate as an introduction. I would however supplement it with "Lectures on quantum theory: mathematical and structural foundations" by Chris Isham. This book is an excellent supplement to whatever a student uses as his/her first book, because it's a short (and cheap) book about what the theory actually says, and not so much about how to calculate stuff.

I think the importance of differential equations is always overstated in these threads, while the importance of linear algebra isn't emphasized enough. It's not a bad idea to take courses on differential equations, but they're not nearly as essential as linear algebra. Students who don't know the basics of linear algebra well will have a lot of trouble with concepts like spin. For linear algebra, I recommend Axler. Some people don't like it, so I will also mention Friedberg, Insel & Spence as an alternative.

Complex analysis is also not essential. I think it's definitely worthwhile to take a course on that topic, but students who haven't can still learn QM and QFT.

I also like Wald and Weinberg, but someone who's going to study GR from Wald, should also read Lee's books on differential geometry and a good text on special relativity. I like the SR sections in Schutz's GR book.

 

[dustytretch]

Wow, I could not have asked for more, thanks for all the help on this!
Now I have an idea about how I am going to tackle the quantum world, the mathematics I need for the task and what texts to look into and not look into.
And also learning classical mechanics as a prerequisite.

My plan of action is to order the M boas book and learn what
maths is needed to use the book.
Then after that I will order one or more of the recommended introductory
texts on QM.

Thanks Timothy Treciokas

 

[Fredrik]

And also learning classical mechanics as a prerequisite.

It's not absolutely essential to study classical mechanics first, but I would still recommend that you do. You should at least make sure that you understand what classical mechanics is. You don't have to be able to solve difficult problems in classical mechanics.

My plan of action is to order the M boas book and learn what
maths is needed to use the book.

I haven't read Boas, so I don't know if that recommendation was good or bad, but my first thought is that it might be better to get a book on calculus (e.g. Lang), and one on linear algebra (e.g. Friedberg, Insel & Spence, or Axler).

 

[dustytretch]

it might be better to get a book on calculus (e.g. Lang), and one on linear algebra (e.g. Friedberg, Insel & Spence, or Axler).

Will these books as well as M boas require a prerequisite knowledge of calculus and linear
algebra to understand?

EDIT: I just had a look at 'A First Course in Calculus' - Serge Lang on amazon, it looks like it needs no prerequisite.

Thanks for the further suggestions!