Help an aspiring physicists what to self-study [closed]

Question

This is probably not the kind of question you'll often encounter on this forum, but I think a bit of background is needed for this question to make sense and not seem like a duplicate:

2012 has been an annus horribilis in my life. I have lost a lot of close relatives in a sudden surge of cardiovascular diseases in my family. I also discovered I inherited genetic diseases and that I'll probably undergo the same fate sooner or later.

One of the people I've lost is my father. We used to talk about physics all the time, and ever since I was 5 I kept telling him my dream was contributing to the field. When I lost him a couple of months ago, I used studying as an emotional outlet. He always emphasized the importance of academic excellence, and for this reason I got obsessed with studying and getting high grades even more than I ever did.

I now am 1/80 in a top high school, but I am frustrated enormously. I find that I waste my time at high school, especially since I probably won't have as much time here as many other people do. I find the mathematics and physics boring and easy, and I feel like I'm wasting my time with certain classes which don't interest me at all (for example Latin). So I decided to study physics and mathematics outside of school. My school has been somewhat supportive, granting me a day per week off to do whatever I want, basically. I of course have a considerable amount of free time in addition to that day, since I ace almost every test without too much studying and without making my homework (not because I don't want to, but because I don't need to).

I decided to self-study because I decided that life is too short (and mine will be even shorter, if I reach 50 I'd be lucky) to waste time. So my plan is to do at least the first 2 years of undergraduate physics in the 2 years I've got left at my high school. My main objective is to gain a mathematical and physical understanding of quantum mechanics, as advanced as I possibly can.

I am currently studying Linear Algebra and Statistics, but I have a problem. I don't know what to study and, especially, in what order to study it. I have read literally read dozens of questions and answers as to what should be the mathematical/physical background for Quantum Mechanics (my future field of interest). But I find these to be too general, and I often am overwhelmed by it. In the same way you can get overwhelmed when you need to clean your house, but it’s so dirty that you don’t know where to start. So I would like your help.

My current mathematical background:

• Basic differential calculus and no integral calculus, we will get that later on this year, however, I think it’s best for me to study it myself before we get it at school since it is crucial in physics. To show my level of differential calculus, this is about the toughest homework question we had to solve algebraically: Given are the functions $f_p(x) = \dfrac{9\sqrt{x^2+p}}{x^2+2}$. The line $k$ with slope $2.5$ touches the function of $f_p$ at point $A$ with $x_A=-1$. Get the function of $k$ algebraically.
• Trigonometry and trigonometric functions. Again, as above, one of the toughest question we had to solve: Given are the functions $f(x)=-3+2cos(x)$ and $g(x)=cos(x-0.25\pi)-2$. Get the functions $s(x)=f(x)+g(x)$ and $v(x) = f(x)-g(x)$ in the form $y(x)=a+bcos(c(x-d))$.
• Analytic Geometry (conic sections, tangency, bisections, you know the drill).
• And of course everything below this level. I probably forgot some things, but you can ask my in the comments if I know certain fields. We will get a lot more mathematics in the coming years, but I want you to disregard that fact when answering that questions. I want to self-study as much as I can, and my mathematics teacher is very fond of me, so if I know a topic before we get it in class, he will let me do other mathematics that I want (he even said this). So I won’t lose time by self-studying subjects we’ll get eventually, so don’t worry about that.

My current physics background (names of the chapters we discussed):

• Newton’s laws, Mechanical energy/forces
• Pressure and Heath
• Signal processing
• Electric currents (Ohm’s law, Series and parallel circuits, etc.)
• Again, everything below this level too (again, I’m probably forgetting stuff). Here exactly the same thing counts as with mathematics, we will get a lot more physics in the coming year, but again, disregard that. My physics teacher adores me, even more so than my mathematics teacher, so again, he won’t mind if I do something else if I know the material he’s discussing already.

This is of higher level than American AP classes and British A-levels, keep that in mind.

Now my question is, what mathematics and physics do I need to study, and my importantly, in which order do I need to study it, in order to have a basic understanding of quantum mechanics in 2 years? I know basic is a very general term, but I think you people, as people who studied it themselves, know what is realistic and achievable. I know this might seem like a duplicate of hundreds of previous questions, but it isn’t. All the other people asking this question have gotten answers that I don’t find suitable for me. Mostly the answers are from people who assume that you have to ‘have a basic understanding of this, a basic understanding of that’, etc. But how do I know what ‘basic means’? Also, now that you guys know exactly what I know and what I don’t, you can more finely tune the answers into my personal situation. As I said, currently I am doing Linear Algebra and Statistics, so you can omit those 2 from your answers, and start from the point I finished those 2 (which will be around January).

• p.s. If you want to recommend certain books, be my guest. If it's a good book, than money is no issue, I've saved up enough money throughout the years

Answer 1

Set your goals on something concrete that you really would like to know but do not yet understand at all, such as ''Why does water freeze?'' or ''What is an elementary particle?''. (And if that is settled, go for something more advanced but again concrete, etc.)

Given the goal, search for the answer, starting with Wikipedia (and later Google Scholar), and backtracking on not or only partially understood concepts and topics until you feel firm ground. This is the only way to see what is important and why. It may take you years to fully understand the answers (some questions of this kind are still poorly understood even on the research level), but it will unlock all your intellectual capabilities, and make you an independent thinker.

The attitude is more important than the order in which you tackle things. Look at my theoretical physics FAQ at http://www.mat.univie.ac.at/~neum/physfaq/physics-faq.html, especially at the first few sections of

Chapter C4: How to learn theoretical physics:

How to become a good theoretical physicist

Learning beyond your level

Learning quantum mechanics at age 14

Physics for self-study while still in school

Research at age 16

Do I always need to have good marks?

Learning scientific concepts

You may also try my online book http://lanl.arxiv.org/abs/0810.1019, for which I got several times feedback from 16 year olds who liked it. If you lack some background, send me an email indicating what you don't understand, and I'll tell you how to learn that.

Answer 2

Your history is deeply moving, so... I apologize for breaking the rules for once, answering here.

First, bear in mind that any life expectancy is a statistical quantity, but every single individual is a statistical fluctuation. If you have, for instance, an expectancy of 20 years in front of you, that only means that the average time left in a set of thousands men in your situation, or if you could rewind and live your life thousands times (that equivalence is called ergodicity) will be 20 years. But for a single individual, nobody can state anything. (After all, this answer turns out to be not fully "unscientific")

Second, please send me a mail. I have very good suggestions on self-learning physics. My address is in one of the comments (I will erase that comment soon).

Answer 3

As I think you are serious, you should start studying mechanics at a higher level, and classical electricity and magnetism.

As I am of an older generation, the books I found good as a preparation for later understanding quantum mechanics and quantum field theory are Classical Mechanics by Goldstein, and Classical Electricity and Magnetism by Panofski and Philips. .

Their formalism in the later chapters is very useful. Maybe somebody younger has a better recomendation.

Answer 4

I will make an unusual suggestion, just because no-one else will suggest proceeding in this way: You should make it your goal to understand the Higgs mechanism, both as a way to give masses to the W and Z bosons, and as a way to give masses to the elementary fermions (the details are different for the two cases).

The Higgs mechanism is a sufficiently advanced concept that to understand it will require you to learn quantum mechanics, special relativity, quantum field theory... so as a goal it is advanced enough to force you to learn all the things that you want to learn anyway. And it is newly validated as an aspect of the real world, so this is the right time to be learning how it works.