How Can a High School Junior Start Learning Quantum Mechanics?

[agent_509]

I am trying to find ways to learn basic quantum mechanics. I am only a Junior in High School, and the only physics course I have taken is Integrated Physics and Chemestry, but I love physics and catch onto it very well. I'm just looking for a place to start learning quantum mechanics that would be suitable, whether it be books, online guides, or videos.

 

[Leptos]

What math do you know so far?

As far as I know, introductory courses for quantum mechanics require that you've at least completed single variable and multivariate calculus, linear algebra, and vector analysis. You may also want to begin with the first year physics sequence(classical mechanics + E&M).

http://ocw.mit.edu/courses/#mathematics
http://ocw.mit.edu/courses/#physics

MIT offers enough open course content for you to progress smoothly.

 

[agent_509]

the only Math classes I've completed in school are Algebra I and Geometry (like I said, I am only a junior in high school), However I have learned some math as I've needed to outside of school for studying physics outside of school. What books would you recommend for learning the different mathematics necessary for learning quantum physics?

 

[Leptos]

What books would you recommend for learning the different mathematics necessary for learning quantum physics?

I would definitely recommend the following Calculus supplements:
Calculus Made Easy by Silvanus P. Thompson
The Calculus Lifesaver by Banner

I suggest buying Calculus 4th Edition by Michael Spivak and the answer manual: Answer Book for Calculus Third and Fourth Edition by Michael Spivak. Spivak is cheap, rigorous, and best for serious students.

https://www.amazon.com/dp/0914098918/?tag=pfamazon01-20

https://www.amazon.com/dp/0914098926/?tag=pfamazon01-20

 

[agent_509]

Thanks for the help! and once I am done with those, where should I start with quantum mechanics?

 

[Leptos]

Thanks for the help! and once I am done with those, where should I start with quantum mechanics?

You should begin with the first year physics sequence: Classical mechanics and then Electricity and Magnetism. High schools sometimes offer courses for AP Physics C which contains either CM, or both CM and E&M.

Also, you can look for old editions of books(+ solution manuals) if you're just trying to self-study material. Schaum's Outlines are very helpful so look for those as well.

Here are some helpful links for Calculus I:
http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx
Keep in mind: The books I mentioned only cover single variable Calculus(Calculus I and Calculus II). For multivariate Calculus(Calculus III), you can buy Calculus on Manifolds by Michael Spivak. You also need to learn Linear Algebra which is typically learned after Calculus II.

People often take Linear Algebra right before, right after, or concurrently with multivariate Calculus.

 

[agent_509]

yeah, I'm mostly looking for self-study material, since I won't be taking basic physics for another two years. anyways, thanks for the help, I greatly appreciate it!

 

[fasterthanjoao]

yeah, I'm mostly looking for self-study material

You should know that quantum mechanics almost certainly isn't what you think it is. Especially the mathematics of quantum mechanics. To do things properly, you're many years behind the level of math that is required - it is very complicated and I wouldn't expect you to even recognise any of the notation that is used, never mind work out what to do with it. It is pleasing that you are so interested in physics that you want to self study - but for things like quantum mechanics I would stick to more popularized literature - go to the book store and pick up some popular science books. Some can be kind of trashy, but others do actually have valuable thought experiments and the like that can get your mind thinking about the kind of things that need to be addressed.

For instance, there are lots of books that cover bits of relativity that are easily accessible to the non-physicist - such books contain wordy explanations for things that would take years to recognise in mathematical terms. I am of the opinion that things like this are valuable too - exposing your mind to lots of different scenarios is extremely important.



If you want to self study something that is relevant and similarly magical, I would look at E&M. EM courses are presented at both introductory level and then again later on in university. I always find that most people hate the introductory (hate is too strong a word) course and find them boring - for some reason students seem to think that EM is outdated or whatever. The same students tackling graduate level EM often come to realize that the subject is one of the most fascinating in all of everything they have done

 

[Elante]

fasterthanjoao makes a lot of good points. I always thought quantum was going to be so cool to take after all the popular science accounts of it, but the class is really nothing like the books: a lot of math. The only really interesting parts of QM when I took it were when we talked about Bell's Theorem, Uncertainty principle, and very briefly, Noether's Theorem. And you can get the gist of these ideas on wikipedia or other books. Finding the solutions to the infinite square well or doing perturbation theory wasn't THAT bad, but... also wasn't all that exciting for me.

Really, I just find the concepts of QM very interesting and philosophically profound, and you don't need all that math to know something about them. Books like "The Elegant Universe" or "A Brief History of Time" is a good place to start.

I agree with fasterthanjoao that intermediate E&M is pretty cool though. For some reason the math in E&M sort of "clicked" with me (lots of multivariable calculus).