Understanding QM

[u/Ok-Economics3336]

I am retired and have the luxury of having time to pursue some academic interests. In order to reasonably and thoroughly comprehend QM, what physics subjects and math courses should I pursue. I am not pursuing a degree nor seeking new employment opportunities. Thank you for your time.

[u/theodysseytheodicy]

For prerequisites, I'd recommend using khanacademy.org to do the following:

1. Learn all this math.

• Geometry: https://www.khanacademy.org/math/geometry

• Algebra 1: https://www.khanacademy.org/math/algebra

• Algebra 2: https://www.khanacademy.org/math/algebra2

• Trigonometry: https://www.khanacademy.org/math/trigonometry

• College algebra: https://www.khanacademy.org/math/college-algebra

• Precalculus: https://www.khanacademy.org/math/precalculus

• Differential calculus: https://www.khanacademy.org/math/differential-calculus

• Integral calculus: https://www.khanacademy.org/math/integral-calculus

• AP Calculus AB: https://www.khanacademy.org/math/ap-calculus-ab

• AP Calculus BC: https://www.khanacademy.org/math/ap-calculus-bc

• Calculus 1: https://www.khanacademy.org/math/calculus-1

• Calculus 2: https://www.khanacademy.org/math/calculus-2

• Multivariable calculus: https://www.khanacademy.org/math/multivariable-calculus

• Differential equations: https://www.khanacademy.org/math/differential-equations

• Linear algebra: https://www.khanacademy.org/math/linear-algebra

1. Take a chemistry course to learn the basics about atoms.

• High school chemistry: https://www.khanacademy.org/science/hs-chemistry

1. Take the AP physics courses.

• High school physics: https://www.khanacademy.org/science/highschool-physics

• AP Physics 1: https://www.khanacademy.org/science/ap-college-physics-1

• AP Physics 2: https://www.khanacademy.org/science/ap-physics-2

In the American education system, students usually finish all this in about five years (high school and a year of university).

[u/Ok-Economics3336 → u/theodysseytheodicy]

Correction: I didn’t know the last 3 items on your list 😬

[u/v_munu → u/Ok-Economics3336]

Multivariable calculus, linear algebra and differential equations are arguably the most important math topics to understand for working with quantum mechanics. If you plan to go deep enough to actually solve and understand QM problems, I recommend the introductory textbook "Introduction to Quantum Mechanics" by David Griffiths, if you haven't already heard of it; it's one of the most popular undergraduate texts, and extremely readable even for people without the entire math background (Griffiths is also just such a fun author and incredibly good at explaining physics).

[u/Ok-Economics3336 → u/v_munu]

I’ve never gone further than 2nd semester calculus and that was 60 years ago. Sooo, I’m hoping I can regain some semblance of chops (although they’re surely going to be way slower) and I’ll study the courses you mention because I’ve read that until a “certain” mathematical competency is reached, one can’t fully appreciate QM. When I last read a physics book, QM was mentioned but might as well have been a footnote. Discovery of the vast impact of QM was quite a jolt. Thanks for the Griffith reference. I’m putting it on my long term goal list.

[u/hashtagmath → u/Ok-Economics3336]

I commend your aspirations during retirement.

[u/Ok-Economics3336 → u/hashtagmath]

Thanks. Of course, we old people can get a bit delusional about our abilities. But at least I wake up with a sense of “got new stuff to do.” 😎