Place to learn mathematics of qm

  • Thread starter Thread starter vuser88
  • Start date Start date
  • Tags Tags
    Mathematics Qm
Click For Summary

Discussion Overview

The discussion centers around resources for learning the mathematics of quantum mechanics (QM), particularly focusing on linear operators and matrix formulation. Participants seek recommendations for books and materials that can provide foundational knowledge in these areas.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant requests recommendations for books to learn the mathematics of QM, specifically mentioning difficulties with linear operators and matrix formulation.
  • Another participant suggests that a solid understanding of linear algebra is necessary before tackling QM, emphasizing the importance of concepts like linear objects, change of basis, eigenvalues, and eigenvectors.
  • Several participants recommend Axler's linear algebra book for its early definition of vector spaces and linear operators, noting its suitability for physics students.
  • One participant mentions that Lang's "Introduction to Linear Algebra" is a gentle introduction that may be beneficial before progressing to Axler, although it may not cover all necessary topics for QM.
  • A participant shares a negative experience with Anton's linear algebra book, criticizing its pedagogical approach and the late introduction of key concepts like vector spaces.
  • Another participant points to Sakurai's "Modern Quantum Mechanics" as a valuable resource for those who have some prior knowledge of quantum mechanics.
  • Zettili's book is mentioned as a reasonable option for covering the mathematical aspects of QM.

Areas of Agreement / Disagreement

Participants generally agree on the importance of learning linear algebra as a precursor to studying QM, but there are differing opinions on which specific resources are most effective. No consensus is reached on a single best book or approach.

Contextual Notes

Some participants express uncertainty about their own mathematical backgrounds and the level of QM they are studying, which may influence their recommendations. There are also varying opinions on the effectiveness of different linear algebra texts, indicating a lack of consensus on the best approach to learning the material.

vuser88
Messages
14
Reaction score
0
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!
 
Physics news on Phys.org
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.
 
vuser88 said:
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.
 
Fredrik said:
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.
 
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.
 
Fredrik said:
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.
 
If you have studied some quantum before, chapter one of Sakurai, 'Modern Quantum Mechanics' is phenomenal for this.
 

Similar threads

Foundations A rigorous approach to learn Mathematics
  • · Replies 20 ·
Replies
20
Views
4K
Intro Math Learning Mathematical Problem Solving
  • · Replies 17 ·
Replies
17
Views
2K
Book on how to define ideas rigorously
  • · Replies 6 ·
Replies
6
Views
2K
Quantum Advanced-undegrad/junior post-grad books on QM mathematics
  • · Replies 3 ·
Replies
3
Views
2K
Study Quantum Mechanics: Recommended Literature
  • · Replies 8 ·
Replies
8
Views
2K
Please recommend a free pdf book about university-level mathematics for me
  • · Replies 5 ·
Replies
5
Views
3K
Foundations Should I start with Lang's Basic Mathematics or Gelfand's books?
  • · Replies 4 ·
Replies
4
Views
9K
Applied A question about mathematics textbooks for physicists
  • · Replies 34 ·
2
Replies
34
Views
10K
What are some recommended textbooks for learning QFT?
  • · Replies 8 ·
Replies
8
Views
4K
Intro Physics What is the best conceptual high school physics book?
  • · Replies 2 ·
Replies
2
Views
2K