Quantum Physics: Mary Boas' "Mathematical Methods" Good?

[entropy1]

I am home studying the basics of quantum physics, starting with Mary Boas' "Mathematical Methods in the Physical Sciences". When I take a look at some of the topics of this forum, there might be better books to start with. Now I am not so sure anymore if this book of Boas is a good book to start with... is it?

 

[Dr. Courtney]

I am home studying the basics of quantum physics, starting with Mary Boas' "Mathematical Methods in the Physical Sciences". When I take a look at some of the topics of this forum, there might be better books to start with. Now I am not so sure anymore if this book of Boas is a good book to start with... is it?

Boas is not a Quantum Mechanics text, although it does contain a lot of the math that will be useful in many Quantum Mechanics courses.

There is a lot of good math in Boas that comes up throughout undergrad and grad level physics courses.

It usually depends on what your background is and what you need the math for down the road.

 

[entropy1]

I got a first-year university diploma IT some thirty years ago, and studied some further before quiting altogether. I got a variety of introductory math topics there like linear algebra, analysis and a few other of which I don't remember the names anymore. I always was very sloppy in practicing (math-)homework. So what I need is practice. However, I am interested in theory too. It has to become a preparation to reading "Introduction to Quantum Mechanics" of David Griffith, which I also have already in my possession.

I am also curious if this book of Boas really is as extensive as she hopes it is.

 

[Andreol263]

Yes, it's a very good book, the only chapter that i recommend to you learn from another book(a proper book on the subject if possible) is Chapter 3:Linear Algebra, the biggest chapter in the book(100pages) and the worse chapter, because it's finish with diagonalization and don't go down on Vector Spaces, Inner Product spaces and so on.., things that you will need to QM, well, for linear algebra pick Linear Algebra Done Wrong by Treil, it's a free book!,and go from the very basics like what are vectors and linear combination to Dual Spaces, Tensors and 'Advanced' spectral theory ;)

 

[Scott Hill]

Boas is a great reference book, but I taught from it once and my students found it difficult to learn from. (My plan was for them to read each chapter, and send me specific topics that confused them, which I would discuss in class. This is not the book to do that with, in my opinion, though of course others may have had more success.)

 

[entropy1]

My current plan is Susskind Theoretical Minimum (nearly finished) - Boas (+Treil ) - Griffiths. Is this a good plan or is there a better one?

Thanks!

 

[entropy1]

I am thinking of trying Ballentine, but which title should I buy as an introduction to QM? (Ballentine seems to have several)

 

[smodak]

I would use these books in order to learn LA and QM
1. https://www.amazon.com/gp/product/3319110799/?tag=pfamazon01-20
2. https://www.amazon.com/gp/product/B00HLW5V9U/?tag=pfamazon01-20
3. https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20
4. https://www.amazon.com/dp/0321765796/?tag=pfamazon01-20

You can also skip 2 & 3 and just do 1 and 4.

Another short book on Linear Algebra that I really like is
https://www.amazon.com/dp/9814723770/?tag=pfamazon01-20

The book is available for free here
https://www.math.ucdavis.edu/~anne/linear_algebra/

Author of #2 has an excellent linear algebra course for free here.
https://www.lem.ma/web/#/books/VBS92YDYuscc5-lK/landing

 

[ZapperZ]

Yes, it's a very good book, the only chapter that i recommend to you learn from another book(a proper book on the subject if possible) is Chapter 3:Linear Algebra, the biggest chapter in the book(100pages) and the worse chapter, because it's finish with diagonalization and don't go down on Vector Spaces, Inner Product spaces and so on.., things that you will need to QM, well, for linear algebra pick Linear Algebra Done Wrong by Treil, it's a free book!,and go from the very basics like what are vectors and linear combination to Dual Spaces, Tensors and 'Advanced' spectral theory ;)

OK, first of all, I highly recommend Boas's text. I've posted several comments to this effect, and even recommended it in my "So You Want To Be A Physicist" essay.

I want to address several issues being brought up here, starting with this one. The problem here is that one needs to carefully look at the intention of the book and who it is aimed for. Note that in the Intro., she is targeting a student who have just completed a sequence of calculus courses and about ready to start on more advanced undergraduate physics/engineering students. She is trying to introduce the students to the "tools" that they might need to start tackling these more advanced classes without scaring them off. So naturally, the level of depth that she can go into, without turning the book into a 10-pound gorilla, is limited. She said so in her Intro:

It is the intent of this book to give these students enough background in each of the needed areas so that they can cope successfully with junior, senior, and beginning graduate courses in the physical sciences. I hope, also, that some students will be sufficiently intrigued by one or more of the fields of mathematics to pursue it further.

This text was never meant to go into the level of detail and depth as, say, Arfken text. And it is also not intended solely for physicists, since her aim is for those in physical sciences, including engineering. Many of the examples in her book are engineering examples.

I've always said that a student shouldn't hear the words "orthonormal" and "eigen values" for the very first time in a QM class. It is extremely daunting to not only learn QM, but also learn the mathematics at the same time. This text tries to introduce such concepts to such students early enough in their undergraduate years before they have to use them. That, in essence, is what this text is for.

Boas is a great reference book, but I taught from it once and my students found it difficult to learn from. (My plan was for them to read each chapter, and send me specific topics that confused them, which I would discuss in class. This is not the book to do that with, in my opinion, though of course others may have had more success.)

But I'm not so sure if there are other text, having the same range of topics, that can do that as well as this text. She has a very conversational tone to her text. In fact, if you look at the Students Solution Manual, it is almost as if she's sitting next to you and telling you exactly why each step of the solution is necessary. I haven't found a book of this type, aimed at students at that level, that is more easily understood than this.

Zz.