How do I start learning quantum physics?

[Hacker4life]

This question has been probably posted a lot of times but I haven't found them.

Where should I start?
There are 2 things I want you to answer me:
Where to start in mathematical part of physics and what to learn and,
Where to start quantum physics after learning the mathematical part of it.

P.S I'm a very fast learner, I don't really like the current school system but I love education.
Don't think I will not understand some things, just shoot me with what you got.

 

[Quantum_man]

Mathematics wise you need to know your algebra really well, some of the rearrangement of the equations can become tricky so you need to be upto scratch. At the university level you need to know differential and integral calculus for physics. For quantum physics you need to start off with the wave-particle duality and start doing simple problems so you can see where the equations fit in and how to solve them.

Once you get into it then you need to be able to solve schrodingers equation for example to solve a particles position in a potential well etc.

Hope that helps

 

[Jano L.]

It may depend on what is your motivation. Do you want to study it because you want to know what new it brought to solution of the problems of physics ? Because it is mathematically demanding? Because it is famous and you want to know what the fuss is about?

 

[jtbell]

Where should I start?

You start from wherever you are right now, of course.

Tell us where that is: how much physics and math have you already studied? Then people can intelligently suggest where you should go next (what you should study next).

 

[Hacker4life]

Jano L:
I want to study it as a hobby, and since I know a few quantum theories and equations I find it very interesting and would like to start learning about it. I was amazed by such things: Double slit experiment, Quantum computers, Quantum teleportation and so on. I don't really understand the equations that go in it so I would like to start with the very beginning. For example: The Bell states are very confusing because I don't know what stands for what. But I could explain them.Quantum_man:
Thanks, it did help but not enough to get started completely.

jtbell:
Lets say that I don't know physics at all, just some elementary stuff.
About my mathematics level, well I'm not sure how to tell you everything that I know. I know how to solve differential equations, I'm going to learn integrals soon, I'm not so good in functions in algebra, I can't say if I know calculus I and II because I have no idea what they are since I'm from another country where they don't mention that.
Can't you just tell me every lesson in mathematics that I need to know before I get started?
And may I say that I like your signature, I have the same opinion about them :D
And about avatars...

 

[ZombieFeynman]

The men who laid the groundwork of quantum theory were masters of classical physics. I think knowing classical mechanics and electrodynamics quite well can put things in context.

 

[Hacker4life]

The men who laid the groundwork of quantum theory were masters of classical physics. I think knowing classical mechanics and electrodynamics quite well can put things in context.

Don't worry about classical physics, it's just along the way. First, I actually do have a basic understanding of it, second if I come in quantum physics to something that is in classical physics I will stop and learn the lesson then continue. It's not hard to me since, as I mention earlier, I understand things fast.

 

[WannabeNewton]

It's insane to do QM without knowing classical mechanics. It certainly "isn't" along the way. Do you know what Hamiltonian mechanics is? What poisson brackets are? How will you appreciate the development of QM without knowing classical mechanics? It's like trying to learn topology without knowing real analysis, you might be able to do it but you won't see the motivation for any of the concepts and/or definitions.

 

[SophusLies]

I agree with WannabeNewton. Also, I want to add that classical mechanics is a beautiful subject in its own right. I remember many me and many of my physics friends thought of it as boring and "old" but little did we know that it would set the framework for QM later on. Focus on learning the basics, if you say you learn fast then what's the big deal about learning what comes before QM?

 

[Hacker4life]

when you talk about classical mechanics, what are you actually talking about, give me some examples?

 

[dx]

Do you recognize this, for example?

dP/dt = -∂H/∂q
dq/dt = ∂H/∂p

 

[micromass]

About the math prerequisites. Please study Linear Algebra before doing QM. And please study theoretical linear algebra (= proof based). It will help you so much. I highly recommend that you go through Lang's "Linear Algebra".

I realize that many people start studying QM without any knowledge of linear algebra, so it's certainly not a "hard" prerequisite. But I would recommend it nonetheless.

You should also be comfortable with, of course, Calc I-III and differential equations. Some say that knowledge of PDE's is necessary, but usually the QM book will teach you the necessary techniques.

As for physics, don't underestimate the importance of Classical Mechanics. I'm sure that QM can be studied as completely stand-alone and not dependent on CM. But this is a very bad approach.
In my point of view, QM is just the noncommutative version of CM. So if you don't know the (easier) commutative version, then you will struggle.

 

[WannabeNewton]

Or this, $\frac{\partial L}{\partial q} - \frac{\mathrm{d} }{\mathrm{d} t}(\frac{\partial L}{\partial \dot{q}}) = 0$. I agree with Sophus, classical mechanics is extremely, extremely beautiful both in its mathematical formalisms and in the physical applications and various physical subtleties (which are the fun parts of course). I see no reason why you shouldn't study it before moving on to QM. It will only benefit you if you intend to study QM in a serious manner.

 

[ModusPwnd]

It's insane to do QM without knowing classical mechanics. It certainly "isn't" along the way. Do you know what Hamiltonian mechanics is? What poisson brackets are? How will you appreciate the development of QM without knowing classical mechanics?

Undergrads generally start with quantum before they do Hamiltonian mechanics or Poisson brackets. I didnt get either of those until graduate school. You certainly don't need them to do Griffiths level quantum mechanics.

 

[WannabeNewton]

Undergrads generally start with quantum before they do Hamiltonian mechanics or Poisson brackets.

You make it seem like just because not all US universities teach Hamiltonian mechanics and proper classical mechanics at the undergraduate level, that it's a good thing. If the OP is interested in a rigorous, mathematical account of QM then an advanced study of classical mechanics cannot be ignored. If he just wants hand wavy accounts of the formalities then yes Griffiths is fine. Actually a book that is not too light on the mathematics but still has great accounts of experiments (the historical motivation in the first chapter is absolutely amazing) as well as physical insights is Zettilli's book.

 

[micromass]

Undergrads generally start with quantum before they do Hamiltonian mechanics or Poisson brackets. I didnt get either of those until graduate school. You certainly don't need them to do Griffiths level quantum mechanics.

I don't think Griffiths is a good book anyway. He will be better off studying classical mechanics including Hamiltonians, and then getting a good book on QM instead of some watered down version.

 

[Hacker4life]

First, I have no idea what the formulas what you guys mentioned are. Second, Can you give me a good book on linear algebra? Third:I really don't know what Calc I-III is so I don't know if I know them. Can you explain it to me? It's a different education system here.

 

[Mmm_Pasta]

First, you aren't ready to learn QM if you do not what those formulas are. You'll most likely need to start from the very basics: a book such as Fundamentals of Physics by Halliday and Resnick.

Second, Micromass suggested one to you.

Third, in the U.S., Calc I-III covers single and multivariable calculus. It's important to study calculus while you study the textbook I mentioned. However, you say your algebra is bad. You'll need to make sure this is good before you start calculus.

 

[ModusPwnd]

You make it seem like just because not all US universities teach Hamiltonian mechanics and proper classical mechanics at the undergraduate level, that it's a good thing. If the OP is interested in a rigorous, mathematical account of QM then an advanced study of classical mechanics cannot be ignored. If he just wants hand wavy accounts of the formalities then yes Griffiths is fine. Actually a book that is not too light on the mathematics but still has great accounts of experiments (the historical motivation in the first chapter is absolutely amazing) as well as physical insights is Zettilli's book.

I make it seem like no such thing. Here is a person who wants to learn some quantum, clearly he doesn't have the background, and you suggest classical Hamiltonian mechanics? Give me a break. Or better, give him a break. Griffiths and Zettilli may seem like trivial beginner books after having studied them, but even they are probably out of the OP's grasp.

Try to put yourself in a non-physics, non-mathematics person's shoes. Browbeating him for having the audacity to want to learn about quantum without having yet studied Hamiltonian mechanics and Poisson brackets is beyond useless, it does a disservice to our attempt at teaching mainstream, non-crackpot quantum physics to the public.

 

[micromass]

I make it seem like no such thing. Here is a person who wants to learn some quantum, clearly he doesn't have the background, and you suggest classical Hamiltonian mechanics? Give me a break. Or better, give him a break. Griffiths and Zettilli may seem like trivial beginner books after having studied them, but even they are probably out of the OP's grasp.

Try to put yourself in a non-physics, non-mathematics person's shoes. Browbeating him for having the audacity to want to learn about quantum without having yet studied Hamiltonian mechanics and Poisson brackets is beyond useless, it does a disservice to our attempt at teaching mainstream, non-crackpot quantum physics to the public.

He recommended Hamiltonian mechanics because he actually cares about the understanding of the OP. I have no idea how a person would possibly understand things like the Schrodinger equation without knowing what a Hamiltonian is.

The inventors of QM were all extremely good in classical mechanics. They had to be to decently develop QM. I think that it would be the best if the students also know the relevant physics before moving on to QM.

 

[WannabeNewton]

I make it seem like no such thing. Here is a person who wants to learn some quantum, clearly he doesn't have the background, and you suggest classical Hamiltonian mechanics?

Yeah exactly, he doesn't have the background. You can't just skip around foundational physics subjects like you're playing hopscotch. I don't get why he has to put off learning the ins and outs of classical mechanics and jump right into QM; moreover the OP said he was doing this for self-study. The OP says he is capable of learning fast and efficiently so the proper route would be to master classical mechanics first and then go on to subjects like QM, treated in a framework that doesn't insult the reader by hand waving everything; the OP says he wants to understand the theory not just know how to solve cookbook problems. Even then, before he learns advanced classical mechanics he has to first learn lower division physics (e.g. Kleppner and Purcell) and basic mathematics (the OP mentioned calculus in particular).

If someone wants to rigorously learn an extensive theory like QM then that person has to take baby steps and make sure the foundations are solid so that he/she can master QM, or what have you, with as much physical insight and mathematical prowess as possible. There's no need to jump right into less rigorous accounts and just settle when it comes to the realm of self-studying.

 

[FeynmanIsCool]

First, I have no idea what the formulas what you guys mentioned are. Second, Can you give me a good book on linear algebra? Third:I really don't know what Calc I-III is so I don't know if I know them. Can you explain it to me? It's a different education system here.

You really need to know calc before trying to understand QM. Calculus I II III Differential equations and Linear Algebra are all required there is no way around it. I my self am a physics major, and I do not fully understand QM (at all!) and as much as one would like to jump right into modern physics, it will be an impossible bridge gap without a strong mathematical foundation and knowledge of classical mechanics. Take your time to learn calc I, then try Linear Algebra, and move onto Calc II and III. Without proper schooling, trying to get to a QM level would be VERY difficult (not saying it can't be done)

DOVER offers a great classic on Linear Algebra

 

[Mentalist]

Fundamentals of Physics by Halliday and Resnick.

2E is the one I used, and then after K&K. But some people go straight to Kleppner first, but I wasn't as advanced at the time in Classical Mechanics (Freshman). But Halliday 2E was good enough as it seems.


As for QM, I haven't taken the course yet, I will be taking it my last semester, which is next spring as I do not have all the prerequisite requirements just yet. But I looked on my schools website to see what book they use, and the book is,

https://www.amazon.com/dp/0471569526/?tag=pfamazon01-20

for those that have read it, is it any good? Also, to micromass, I was going to pick up Griffiths book just to read it over the summer because I heard some good things about it. You disagree, I know, but what do you recommend?

 

[dextercioby]

Cohen-Tannoudji's book has the virtue of being encyclopedical (lots of subjects in 1400 pages), but the book's presentation makes it a poor textbook. So you have 2 options: keep it and rely on the professor's presentation, or ignore it and try some shorter, better written version, like N. Zettilli's account.

 

[bhobba]

I don't think Griffiths is a good book anyway. He will be better off studying classical mechanics including Hamiltonians, and then getting a good book on QM instead of some watered down version.

I agree. To the OP check out:
https://www.amazon.com/dp/046502811X/?tag=pfamazon01-20

It covers both the math and foundational physics to start doing real deal QM.

The book I like after that is Quantum Mechanics Demystified:
https://www.amazon.com/dp/0071455469/?tag=pfamazon01-20

I have the book - its easy to understand and cheap. But it does have a few typos which strangely I don't mind - it keeps you on your toes - by saying that's wrong and figuring out why you learn a lot.

Then some of the free stuff around to bring your math up to a good level eg:
http://zippy.ph.utexas.edu/~msihl/teaching/PHY389K_F06/chapter01.pdf

Finally, with that background, Ballentine will provide an excellent foundation at a more advanced level:
https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20

It will take a while to work through it but when finished an understanding of QM to a very good level will be the result.

Thanks
Bill

 

[Hacker4life]

Wow, you people are way too awesome. I never expected you to take this thread that seriously. Thanks to everyone.
===================================
When I asked what Cacl I, II, III are, I meant what lessons are in them, I am currently in a special mathematics class where we learn advanced lessons in mathematics. When I said I don't know linear algebra I meant that I don't know advanced linear algebra good.

So, the answer is yes, I will start from the beginning and not skip if I don't know something.
But still, you recommended a lot of books here, so could you tell me what book would you recommend me as a beginner?
So, don't tell me about the books about quantum physics.

What book would you recommend for me? There are a lot of books here so I'm not sure which one to get?

 

[bhobba]

Susskinds book the Theoretical Minimum to start with:
https://www.amazon.com/dp/046502811X/?tag=pfamazon01-20

It covers the math and material such as Poisson Brackets and Hamiltonian's necessary for a serious study of QM.

Thanks
Bill

 

[dx]

Watch Susskind's video lectures too, they're very good. He has lectures on classical mechanics as well as quantum mechanics.

You can find them on youtube and also on itunes.

 

[micromass]

Watch Susskind's video lectures too, they're very good. He has lectures on classical mechanics as well as quantum mechanics.

You can find them on youtube and also on itunes.

The video lectures are quite good. But please don't use only the video lectures. You should mainly use textbooks. Video lectures should be a secondary resource. I think the most important thing to do is to do as much problems as possible.

 

[dx]

Agreed. You should also know that the lectures are "specifically aimed at people who know, or once knew, a bit of algebra and calculus, but are more or less beginners"

They will get you started but you should consult other resources and more detailed books with problem sets etc.

 

[eloheim]

Just ran into this thread. Much appreciation to the patient responders (esp. on such a long-trodden road as this one).

I thought I'd share my experience that ignorance of the maths invoked here is greatest hurdle to any exploration of physics in a field other than classical mechanics, certainly in part because the 'standard process' prescribes the two (classics phys and calculus) to be co-requisite, and the introductory (collegiate) physics material reflects this assumption of parallel development.

The flip side of this though is that the robust mathematical repertoire (from what I gather--still working on it!) mentioned in previous posts allows one broad and great access to many facets of not only modern physics but throughout the whole of science.

Unfortunately (as I found) the raw time constraints imposed by Life makes taking the years to bring one's maths up to snuff a considerable investment, and (IMHO) the biggest obstacle to picking one's own way through the physics menagerie. A few years ago I was in a similar position to that of the OP, and eventually decided that--at least in beginning--the slow-and-steady traditional path was necessary, or at least the best option available, considering all the factors. Certainly not sexy: Classical Physics I and Calculus I...

En rout to my decision, I did discover that there ARE authors interested in reformulating the educational path in physics, with less of dependence on rigidly segregated classical foundations. They usually took the perspective of relaxing the chronological (historical) progression of the standard sequence in favor of a presentation based on their own preferred unifying principle(s).

One I found is called "A Radically Modern Approach to Introductory Physics," by Raymond:

The course includes students intending to major in physics, but is not limited
to them. The idea for a “radically modern” course arose out of frustration
with the standard two-semester treatment. It is basically impossible to incorporate
a significant amount of “modern physics” (meaning post-19th century!)
in that format. Furthermore, the standard course would seem to be
specifically designed to discourage any but the most intrepid students from
continuing their studies in this area — students don’t go into physics to learn
about balls rolling down inclined planes — they are (rightly) interested in
quarks and black holes and quantum computing, and at this stage they are
largely unable to make the connection between such mundane topics and the
exciting things that they have read about in popular books and magazines.

I tried a couple of these but ultimately I felt 'neutered' without a real understanding of the mathematical sub-structure holding all of it up. Once I realized the magnitude of the undertaking (I'm talking Calc I-III+Diff EQ+a bit more, perhaps), I realized I might as well be studying what physics I can without such knowledge: namely Classical Mechanics. And 'whala:' I'm your standard undergraduate physicist! :tongue: