Place to learn mathematics of qm

[vuser88]

hello there, i need a place or a book where i can learn the mathematics of QM.

I am having trouble with linear operators and matrix formulation.

Like how do you represent an operator? How can one jump between operators and then back to matrix formulation.

I NEED THE BASICS!


Thanks!

 

[chiro]

Hey vuser88 and welcome to the forums.

It might help us if you tell us your mathematical background as well as the level of QM you are studying (introductory, advanced, and specific details).

If you are unfamiliar with linear objects (operator, map, etc) then you need to learn linear algebra first before you start learning QM. Learning linear algebra in some depth will help you answer questions relating to the understanding of linear objects including things like change of basis and eigen-values and eigenvectors which are also critical to know.

For a linear algebra text or other resources I would suggest that you search the forums as there are many people here who are mathematicians and physicist who have studied this in more depth and some here teach these subjects which means that are going to be more familiar with a good introductory text.

 

[Fredrik]

hello there, i need a place or a book where i can learn the mathematics of QM.

I am having trouble with linear operators and matrix formulation.

Like how do you represent an operator? How can one jump between operators and then back to matrix formulation.

I NEED THE BASICS!


Thanks!

The relationship between linear operators and matrices is explained e.g. in post #3 in this thread. (Ignore the quote and the stuff below it).

Most books on linear algebra should be able to teach you the basics. I recommend Axler. It defines vector spaces and linear operators right at the start, unlike e.g. Anton which doesn't define linear operators until around page 300 (in the old edition that was used when I first studied linear algebra). I can't get over how bizarre that is. I also think the selection of topics in Axler's book is appropriate for a physics student. If you for some reason don't like it, the main alternatives are probably Friedberg, Insel & Spence, and Hoffman & Kunze.

 

[Broccoli21]

I recommend Axler. It defines vector spaces and linear operators right at the start, unlike e.g. Anton which doesn't define linear operators until around page 300 (in the old edition that was used when I first studied linear algebra).

I couldn't agree more. Axler is a great book, and is perfect if you want to understand operators better. You might also want to learn some basic PDEs, if you haven't already.

 

[qspeechc]

A very gentle introduction, but still good quality, appropriate for people who are not maths majors or maths whizzes, is Lang's "Introduction to Linear Algebra". Some good features of the book are the diagrams (rare in maths books and especially Lang) and the answers at the back of the book. But the book is very elementary, and won't get you up to the level you need for QM. A very good book to follow this with is Axler, as mentioned before.

If you are having trouble with a math book like Axler, or any other linear algebra book, I recommend you read Lang's book first.

 

[czelaya]

The relationship between linear operators and matrices is explained e.g. in post #3 in this thread. (Ignore the quote and the stuff below it).

Most books on linear algebra should be able to teach you the basics. I recommend Axler. It defines vector spaces and linear operators right at the start, unlike e.g. Anton which doesn't define linear operators until around page 300 (in the old edition that was used when I first studied linear algebra). I can't get over how bizarre that is. I also think the selection of topics in Axler's book is appropriate for a physics student. If you for some reason don't like it, the main alternatives are probably Friedberg, Insel & Spence, and Hoffman & Kunze.

I've been wanting to refresh on linear algebra (it's been about 5 years). I took a course on linear algebra using Anton. It was a painstaking process, at times, the book seems to congeal a slew of ideas into a pedagogical mess. The way the Cauchy-Schwartz's inequality is introduced is dreadful, and had me pacing in my room for days.

By the way, in the 9th edition(Applications Version), vector spaces aren't introduced until the 5th chapter. By this time in the course I could calculate, but didn't have a firm grasp of the theory.

 

[Jorriss]

If you have studied some quantum before, chapter one of Sakurai, 'Modern Quantum Mechanics' is phenomenal for this.

 

[physiker_192]

Zettili's book covers those things:
https://www.amazon.com/dp/0470026790/?tag=pfamazon01-20

I found it to be reasonable in covering the mathematical aspects, but that's about it.