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Robert Arthur
By now you’ve probably gathered that self-learning your way to PhD-level understanding of quantum mechanics (or anything else, really) is almost impossible. But that does not mean that you cannot teach yourself to understand PhD-level quantum mechanics. These are two different goals.
This is what I’m currently working towards in my spare time, as I simply cannot afford to leave my job and return to full-time study. And I am getting there, though it has taken years so far, and cost me a small fortune in textbooks. So I’ll tell you some of the things I learned the hard way.
Maths.
I have an advanced degree in pure mathematics, so I thought I’d walk that part. But it turns out the sort of maths I specialised in—(semi)group theory—has been of little use to me until now. And while I certainly understood the necessary techniques, such as differential/integral equations, vector calculus, linear algebra etc., I was horribly out of practice. While you might think that if all you want to do is learn the concepts, and have no intention of ever needing to apply them, that you could skip this part, you would be wrong. You have no hope of following a textbook without following the derivations closely.
So if your mathematics isn’t up to scratch, that’s where you start. The topics I mentioned above are essential, and this is one area you’ll want a decent MOOC-like course, such as edX, with assessed homework to keep you honest.
Breadth, not depth.
When I started, I wanted to learn about quantum mechanics. I wasn’t particularly interested in areas like electromagnetism, classical mechanics or thermodynamics, beyond what I learned at school. So I aimed narrow. Bad choice. It resulted in numerous “false starts”, where I had to abandon what I was doing and start again with a better foundation.
For example, MIT’s famous first-year lectures 8.0[1–3] (with Professor Walter Lewin) are available online, and well worth watching, despite the lousy video quality. They cover the basics of classical mechanics, electrodynamics and waves, and are a bare minimum for anything quantum, but even they are streamlined for students following a learning path. You’ll be finding your own way, and will have no idea what topics can be safely skimmed over without coming back to haunt you later. So use the videos/courses, but they will almost certainly need supplementing with textbooks.
(Incidentally, I believe a new version of MITx’s 8.01 Mechanics/Kinematics course is starting October 2016; probably worth looking at if you’re around that level)
Classical does not mean easy.
As mentioned above, you will need a good foundation in classical mechanics and electromagnetism to get anywhere in quantum physics. But don’t think that once you start learning some quantum mechanics that you’re done with the classical stuff. Some topics in classical subjects are significantly more advanced than, say, a first course in quantum mechanics. So be prepared to go back and forth on topics, and be careful when buying books that you know the level they are aimed at.
Books.
Bottom line is there are not yet enough online courses to cover a full degree’s-worth of topics, and as mentioned above, the ones there are will not even cover their own topics to the level you will need. So you will be buying an awful lot of books. First step: if you do not already own a tablet computer, buy one now. Paper books just aren’t practical for what you need. They take up too much room and they don’t travel well, but more importantly they are not searchable, and unless you’re content to scribble all over your texts, they’re no use for annotating/bookmarking. As a student, these things are less of an issue; you’ll generally be given a few selected chapters from one or two texts at a time. When self-learning, you’ll be reading books cover to cover (sometimes repeatedly before it sinks in).
You should also prepare yourself to read multiple texts on the topics you are studying. Authors each have their own approach to their subject, so to be sure you are ready to progress to more advanced topics; you may need to get used to a range of techniques and notations. Moreover, advanced texts will not pick up from where you left the more basic ones; there may be significant overlap, but you will have to go through it again if you want any chance of comprehending the later topics. It gets easier, though; once you’ve seen the eigenstates of the hydrogen atom derived four different ways, you’ll start to sing along!
Although I stated above that e-books are to be preferred, this is not always straightforward. Many of the seminal texts in all areas are not available as e-books. You will have to decide between getting a physical copy of these, or trying to find an e-book alternative. And it doesn’t end there: e-books come in many flavours. My iPad currently has six different e-book apps installed (GoodReader, Kindle, Google Play, iBooks, Adobe Digital Editions and VitalSource), and the quality varies greatly between them. Kindle books often (not always) render text just fine, but have equations embedded as low-quality images. Google Play books tend to use scanned pages combined with OCR for searching; the ones I bought look as though they’ve gone through a blur filter in places. ADE books look fine, but their DRM limits your choice of reading app.
If given the choice, try to find books that can be downloaded as DRM-free .pdfs. These always have the best quality rendering, and a wide range of readers. Some publishers (Springer, notably) offer watermarked .pdfs; you will come to love them for it. Whatever format you find, always check out a sample chapter if available.
That’s all I can think of for now—if anything else occurs to me, I’ll update my answer. In the meantime, I hope you are not too daunted by the answers here; this stuff is not easy, and there are no shortcuts, but that’s never a reason not to try. Good luck!
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By now you’ve probably gathered that self-learning your way to PhD-level understanding of quantum mechanics (or anything else, really) is almost impossible. But that does not mean that you cannot teach yourself to understand PhD-level quantum mechanics. These are two different goals.
This is what I’m currently working towards in my spare time, as I simply cannot afford to leave my job and return to full-time study. And I am getting there, though it has taken years so far, and cost me a small fortune in textbooks. So I’ll tell you some of the things I learned the hard way.
Maths.
I have an advanced degree in pure mathematics, so I thought I’d walk that part. But it turns out the sort of maths I specialised in—(semi)group theory—has been of little use to me until now. And while I certainly understood the necessary techniques, such as differential/integral equations, vector calculus, linear algebra etc., I was horribly out of practice. While you might think that if all you want to do is learn the concepts, and have no intention of ever needing to apply them, that you could skip this part, you would be wrong. You have no hope of following a textbook without following the derivations closely.
So if your mathematics isn’t up to scratch, that’s where you start. The topics I mentioned above are essential, and this is one area you’ll want a decent MOOC-like course, such as edX, with assessed homework to keep you honest.
Breadth, not depth.
When I started, I wanted to learn about quantum mechanics. I wasn’t particularly interested in areas like electromagnetism, classical mechanics or thermodynamics, beyond what I learned at school. So I aimed narrow. Bad choice. It resulted in numerous “false starts”, where I had to abandon what I was doing and start again with a better foundation.
For example, MIT’s famous first-year lectures 8.0[1–3] (with Professor Walter Lewin) are available online, and well worth watching, despite the lousy video quality. They cover the basics of classical mechanics, electrodynamics and waves, and are a bare minimum for anything quantum, but even they are streamlined for students following a learning path. You’ll be finding your own way, and will have no idea what topics can be safely skimmed over without coming back to haunt you later. So use the videos/courses, but they will almost certainly need supplementing with textbooks.
(Incidentally, I believe a new version of MITx’s 8.01 Mechanics/Kinematics course is starting October 2016; probably worth looking at if you’re around that level)
Classical does not mean easy.
As mentioned above, you will need a good foundation in classical mechanics and electromagnetism to get anywhere in quantum physics. But don’t think that once you start learning some quantum mechanics that you’re done with the classical stuff. Some topics in classical subjects are significantly more advanced than, say, a first course in quantum mechanics. So be prepared to go back and forth on topics, and be careful when buying books that you know the level they are aimed at.
Books.
Bottom line is there are not yet enough online courses to cover a full degree’s-worth of topics, and as mentioned above, the ones there are will not even cover their own topics to the level you will need. So you will be buying an awful lot of books. First step: if you do not already own a tablet computer, buy one now. Paper books just aren’t practical for what you need. They take up too much room and they don’t travel well, but more importantly they are not searchable, and unless you’re content to scribble all over your texts, they’re no use for annotating/bookmarking. As a student, these things are less of an issue; you’ll generally be given a few selected chapters from one or two texts at a time. When self-learning, you’ll be reading books cover to cover (sometimes repeatedly before it sinks in).
You should also prepare yourself to read multiple texts on the topics you are studying. Authors each have their own approach to their subject, so to be sure you are ready to progress to more advanced topics; you may need to get used to a range of techniques and notations. Moreover, advanced texts will not pick up from where you left the more basic ones; there may be significant overlap, but you will have to go through it again if you want any chance of comprehending the later topics. It gets easier, though; once you’ve seen the eigenstates of the hydrogen atom derived four different ways, you’ll start to sing along!
Although I stated above that e-books are to be preferred, this is not always straightforward. Many of the seminal texts in all areas are not available as e-books. You will have to decide between getting a physical copy of these, or trying to find an e-book alternative. And it doesn’t end there: e-books come in many flavours. My iPad currently has six different e-book apps installed (GoodReader, Kindle, Google Play, iBooks, Adobe Digital Editions and VitalSource), and the quality varies greatly between them. Kindle books often (not always) render text just fine, but have equations embedded as low-quality images. Google Play books tend to use scanned pages combined with OCR for searching; the ones I bought look as though they’ve gone through a blur filter in places. ADE books look fine, but their DRM limits your choice of reading app.
If given the choice, try to find books that can be downloaded as DRM-free .pdfs. These always have the best quality rendering, and a wide range of readers. Some publishers (Springer, notably) offer watermarked .pdfs; you will come to love them for it. Whatever format you find, always check out a sample chapter if available.
That’s all I can think of for now—if anything else occurs to me, I’ll update my answer. In the meantime, I hope you are not too daunted by the answers here; this stuff is not easy, and there are no shortcuts, but that’s never a reason not to try. Good luck!
See Questions On Quora
Continue reading...
