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I am a current high school student and I am very interested in physics, especially particle physics (that stuff is super cool!). Unfortunately, my school only teaches classical physics, so I have to continue my study at home. I've read several books and watched videos and online lectures on quantum mechanics and have gotten a basic overview of the big ideas, but when I try to dig even just a little bit deeper the math immediately gets too confusing to handle. Beyond basic summaries and oversimplifications, what other resources can I use to continue studying physics but avoid getting frustrated by math that I don't understand?

EDIT

Based on feedback so far, I think the question I should really be asking is "What are some resources that can help teach me the prerequisite math I need to know for quantum mechanics?"

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    $\begingroup$ Unfortunately, my school only teaches classical physics do most high schools go further? $\endgroup$
    – BioPhysicist
    Commented Jul 17, 2019 at 3:29
  • $\begingroup$ I don't think so, but they totally should! A lot of students are missing out on the awesomeness of physics! $\endgroup$
    – Morrison Bower
    Commented Jul 17, 2019 at 3:32
  • $\begingroup$ @AaronStevens I actually had a friend who taught QM at high school - but it was to a special class of the best students as part of Olympiad prep. $\endgroup$
    – Allure
    Commented Jul 17, 2019 at 3:35
  • $\begingroup$ Does your school teach calculus? $\endgroup$
    – G. Smith
    Commented Jul 17, 2019 at 3:54
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    $\begingroup$ My suggestion is to pursue your self-study on two tracks: (1) “Popular” and math-free, but accurate, books about the concepts and history of physics. (2) Calculus to the point where you understand what derivatives and integrals are, how to do basic calculus calculations, and what a differential equation is. But don’t neglect your class studies or you’ll get poor grades and never get into a university with a decent physics department. Getting into a good university is more important than learning physics a few years early. $\endgroup$
    – G. Smith
    Commented Jul 17, 2019 at 4:08

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Now is not the time to worry about quantum mechanics. There's a reason it's not taught at high school: it's not a simple topic, and you need prerequisite mathematics (especially calculus & linear algebra) that takes time to learn.

If you must attempt it anyway then in my experience the most common QM undergraduate textbook is David Griffith's Introduction to Quantum Mechanics. However, as mentioned, you will have trouble understanding this book without the prerequisite mathematics.

I suggest not feeling bad about it though, because when I did undergraduate studies, the program left QM to 2nd year, with the first year spent making sure everyone had the necessary mathematics.

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Unfortunately, my school only teaches classical physics

Good to hear that, because you cannot understand the physics of quantum theory without a very solid understanding of classical physics. That understanding will have to go well beyond the level of classical physics taught in high school.

There are certainly mathematical tools that you need as a minimum in quantum theory, but these tools don't help you if you do not understand the core physics really well.

An firm understanding of the concepts (not the mathematics) of Thermodynamics, Electromagnetic theory and Classical mechanics will serve you a great deal more than knowing the fancy mathematics. Why ? Because the reason you end up with equations of a particular form in quantum theory is because of the need for the results to conform to these other concepts.

You also tend to pick up the mathematics you need for quantum theory in learning these things.

If you want to make a "small investment" in mathematics (that won't interfere too much, if at all with your high school studies) I would recommend learning :

  • Basic of Group Theory
  • Basics of Complex Numbers
  • Trigonometry
  • Basic calculus - differentiation, integration

These are all typically taught to a useful level in higher level High School mathematics courses these days.

So what you might do is (maybe) talk to your High School mathematics teachers and ask if you could get a start on the higher level mathematics I mentioned.

G Smith mentioned that it's extremely important you put equal (if not more) effort into the non-physics and mathematics because you need the good results in those (at the very least) to get into university or a technical school. You also need them because, in the real world, having these other skills turns out to be rather important in terms of getting good jobs, being able to perform well at business (even physicists have to do interviews, business meetings, write reports, and so on). They round out your skill set and help a lot - don't neglect them. To put this in some perspective, my university physics course had mandatory courses in business skills (e.g. basic accountancy) which also came with a requirement for mandatory passes and contributed to your final degree grade. These things are important and the skills served me well.

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Ah I remember my high school days of yearning to learn complex physics (it was only 10 years ago lol). I’d start at one Wikipedia page and go from page to page trying to understand something but having to try to understand something else first. It was a lack of prerequisites as Allure said. If that happens, don’t let it frustrate you. I also recommend Griffiths but yes, you’ll need to understand linear algebra and calculus to get through it (integrals and partial derivatives are everywhere in quantum)

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