I have taught myself quantum physics but without the math. In other words, I can calculate only the tiniest bit of anything quantum mechanical, but I have some understanding of quantum physics concepts. I also have a conceptual understanding of some of the equations. However, I believe that if I continue my studies, I will be able to do quantum physics calculations. I have a college degree but no college math or physics. Actually I’ve never taken a physics course in school.

It’s taken me about 4 years, very part-time, to get through a basic understanding of classical physics, quantum physics, a review of high school math, and first year calculus. I have about average talent at math (though I really enjoy it), a below average talent at classical physics, and some talent at quantum physics.

What it takes is an intense interest in quantum physics, patience, perseverance, and, at least some of the time, enjoyment of the learning process. All the on-line resources I describe below are free. I bought books from Amazon.

Classical Physics First

To understand quantum mechanics, it’s necessary to first understand regular physics (classical physics). This is because much of classical physics applies to quantum physics. When it doesn’t apply, you’re supposed to be surprised. If you don’t know classical physics and aren’t surprised, you’re not going to get what’s so unique about quantum physics—you’re not going to get why physicists are puzzled and what puzzles that they’re trying to resolve.

I studied classical physics at PhysicsClassroom and Khan Academy. I started with kinematics and kept going until I felt that I had the basics. I also worked my way through a physics textbook, reading and doing the problems: Physics and Society by Art Hobson, published by Pearson, available on Amazon in softcover. This is an extremely brief review of classical physics and an introduction to relativity and quantum physics. A basic understanding of relativity is important to some aspects of quantum physics.

The on-line courses are free. These resources provide practice problems with answers so that you can check your work. No calculus needed.

Quantum Physics

I started my study of quantum physics with videos on Youtube. These are at all different levels. I only watched ones intended for laypeople. They have little or no math. I suggest starting with the series “Looking Glass Universe” and “Cracking the Nutshell.” Try to find the first videos on quantum mechanics in each series and go from there. I also watched a huge hodgepodge of other videos until I felt oriented.

I also read biographies of the early quantum physicists. These biographies included a little science—a good way to get your toes wet. The history of quantum physics very much helps in understanding the field. This is because you’ll run across many conflicting descriptions of quantum physics principles. They were either written by quantum physicists in different time periods or written by non-physicists who don’t know that the time period matters. This can be confusing unless you understand that views of quantum physics have changed over the years.

Then, I read books for laypeople on quantum physics. The best ones so far have been Quantum, a Guide for the Perplexed (Jim Al-Khalili) and Understanding Our Unseen Reality (Ruth E. Kastner). Both authors are working quantum physicists, but the books are written for non-physicists.

Math

Even if you want to learn quantum physics at only a conceptual level, like I have, it is desirable to have some understanding of calculus. It may not be essential, but it very much helps. For me, it gives me a general understanding of the quantum equations even though I couldn’t possibly solve them. (I plan to keep going with calculus and maybe one day I will be able to solve them.)

Each day, I study math for about half an hour and I study or write about quantum physics for about an hour.

I reviewed a lot of math on the Khan Academy website. I knew that I needed work on manipulating fractions, logs, and exponents. You will need these skills for calculus. You don’t need much geometry but you do need trigonometry and algebra. However, I started calculus without reviewing trig and algebra.

After reviewing fractions, logs, and exponents, I started the free on-line Ohio State first year calculus course (Calculus 1 On-Line Lessons). When I ran into difficulties because of insufficient algebra or trig, I went back to Khan Academy and also Paul’s On-Line Notes and Math Is Fun.

If I need more practice problems for calculus than the Ohio State website provides, I go to one of these other math websites that I’ve mentioned. I also google “problems and solutions” for whatever type of problem I’m looking for. There are lots of these on-line that instructors kindly supply.

Keys to Success

1. As your question suggests, take things step-by-step. Study at least some classical physics before quantum physics. Study algebra and trig before undertaking calculus.
2. In math, master each step before going on to the next. If you understand a subject, you should be able to do problems without errors. If you can’t do the problems or make a lot of “careless” errors, it means that you’ve not achieved mastery. I learned something—careless errors mean that you’re still struggling with the concepts. This is true for both physics problems and math problems.
3. Look up words that you don’t understand. This may mean looking them up over and over. That’s what I’ve done. This is true for both regular English words and technical words. For technical words, find pictures and animations. Usually, Wikipedia is too technical, but it provides good pictures and animations. Pictures and animations are really important for understanding physics and, sometimes, math. Also, find pictures and animations by googling. Google your topic and then, click Images or Videos. Also, search on Youtube. I’m writing an encyclopedia of quantum physics for non-mathematicians on this website. It’s not yet complete, but you can find definitions of many classical and quantum physics terms there.
4. If you find a good resource at your level, but you think that you could get more from it, do it over… and over. I’ve watched short videos 8 and 9 times. I’ve read most of my quantum physics books at least twice, one 7 times!
5. If you find that what you’re studying is confusing or that you’re blanking out or getting less and less out of it, stop moving forward. Find where you were last doing very well. Find at the end of where you were last doing really well, what didn’t you fully get? Was it a word (regular English or technical)? Do you need to look at pictures or animations? Do you need to work problems? Fix the issue. And then, move forward again from that point. Or you may decide that this resource is just too challenging and find another that suits you better.
6. This doesn’t mean that you must master each part of quantum physics before going on to the next. This is true for math, but not quantum physics. With math, unless you master each step, you’ll crash on the next one. But quantum physics is different. I cycle through videos/books on quantum physics, getting what I can from each and deciding upon completion if I want to re-do it immediately or move on to another and, possibly, come back later. My understanding of quantum physics has built up by reading different authors, watching different videos, and just getting the feel for what is going on.

Understanding quantum physics in a conceptual way doesn’t take great talent or college training—I’m the proof of that. It takes a lot of exposure to the concepts from many different viewpoints. And it takes patience, determination, and a willingness to tolerate counter-intuitive ideas.

For me, the notion that “no one understands quantum physics” isn’t true. Through all the exposure to various authors’ viewpoints and by trying to explain it all to my husband and also by writing my quantum physics encyclopedia, I’ve built up an ability to visualize what is going on. I’ve built up a feel for how it all works.

I find quantum physics an extremely rewarding field to understand. I want to know how this universe works. Quantum physics is one path in that quest. I feel that the more people understand quantum physics, the more able they are able to perceive the truth of what is really going on. I’m not going to explain that last statement. It may become clear when you study quantum physics.

I hope that what I have written will help you (and others) to decide if you want to study quantum physics. If you decide to undertake it, I truly wish you luck and good results. If you run into problems, you can always ask another question on Quora or search the many answers to Quora questions about quantum physics.