Learning QM and the math required.

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In summary, the conversation is about the individual's attempt to relearn QM after a lengthy layoff and their concerns about not remembering the necessary math skills. They mention having taken grad classes on Quantum Chemistry and their goal of understanding grad level discussions. They also discuss various textbooks and resources they are using, as well as their motivation for getting back into QM. They mention their math background and compare it to the person they are conversing with.
  • #1
ChemGuy
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I am trying to learn/relearn QM after a lengthy layoff (10+ years). I have had calc and diff EQ and partial Diff EQ but to be honest I don't remember the details anymore. For example I don't remember any of the standard solutions to integrals. I understand the principles but am just out of practice of actually doing it. I can follow along in a text ok but don't ask me to independantly solve the problems... the memory is just not there. I had actually taken a grad class or two on Quantum Chemistry so I know I could do it at one time!

Here is the question. Is it possible to learn QM and QFT principles without the detail technical ability? I have access to textbooks but it would take forever to go back over them to bring myself back up to math speed. I am not looking to be a master on these subjects but I am trying to be able to understand grad level discussions. Thanks.

Ed
 
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  • #2
First thing is to choose right books concentrating on physics and not in linear algebra or integrals, for example the green textbook by Dirac (foundations of qm or something?).

For QFT, in my opinion, some mathematics are needed as it is very hard to find texts where things would be explained correctly without rigorous calucations.

Anyways, physics is physics and math is math, so there is hope.
 
  • #3
Nah, there's too much mathematics hidden in the axioms of QM (or QFT) that you can never say you fully understand them without understanding the maths.

Daniel.
 
  • #4
There aren't a whole lot of options. Most books that try to explain it without using math are not very good. The reason is because the concepts are largely mathematical, and do not translate well into plain English. So most mathless books tend to be general summaries of how the concepts have evolved over time (wasting space with what we used to think, rather than what is now thought), or try to explain the concepts with analogies that aren't really accurate, and don't give a real understanding.

If you are really interested, though, I would recommend Penrose's book "The Road to Reality." It is over a thousand pages long, and is full of math. But he teaches you the math you need, as you go along. You'll be deep into imaginary/complex numbers before you know it. This book really was designed for people like yourself, and I think you might get a lot out of it. There are problems to solve, if you feel like it, but you don't have to in order to keep proceeding through the concepts. Just take a moment to ensure you understand what the equations are saying (and he does a good job of building up your understanding, step by step), and you'll get it.

Hope this helps.
 
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  • #5
I actually think I am somewhere in between the two worlds. It is not the general concepts of the math but the details. For example if a problem required integration by parts I could recognize that it was required but I would have to go look for the formula to do it. That is a trivial example but I think you get my point. It seem a waste to have to go back and relearn all the techniques to be able to understand the concepts the QM is about. No granted that I will have to learn some stuff like linear algebra (which I never go around to) but I expect that.
 
  • #6
I'm also trying to relearn QM after about the same layoff.

It sounds like what you need is a book with lots of solved problems. There's a Schaum's outline on QM which get's middling reviews, but may be enough to get you started. I'm starting to work my way through Problems in Quantum Mechanics by Squires.

I wouldn't worry too much about the math. It should start to come back as you work problems. Inability to remember arcane integrals should not be a problem; just get the Schaum's Mathematical Handbook and keep it handy.

By the way, what text are you trying to learn from?
 
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  • #7
I am using a "popular" book that has gotten poor reviews. It is by David McMahon. I think it got bad reviews because there are a million typo errors in it. I think it is making me look harder at each step in the solution. It does a pretty good job of explaining the steps but of course not perfect. I looked at Squires book but it doesn't look like there are any explanations. Is there or is it just a problems book.

If you don't mind, what is your motivation for getting back into QM? Is your background (math wise) similar to mine?
 
  • #8
I've paged throught the McMahon in the bookstore. It looked like it was pretty much a condensation of the typical undergrad QM text.

You've probably already found the errata on the http://www.quantumphysicshelp.com/quantum_physics.htm , though I don't know why there's only errata for 2 chapters.

The Squires book has problems and complete solutions with a brief summary of the material at the beginning of each chapter, but only enough for reference while doing the problems. The value of a book like this is that you can check your work against the solutions, or peek if you get totally stuck.
 
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  • #9
ChemGuy said:
If you don't mind, what is your motivation for getting back into QM? Is your background (math wise) similar to mine?

I wanted to learn some QFT, or at least QED, something I never got to in grad school. I found, though, that I'd forgotten a lot of QM, and probably never knew some of it very well (e.g. scattering theory). As for math background, I have 15-year old undergrad degrees in math and physics, with a few years of graduate physics courses (Goldstein, Jackson, and all that).
 
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  • #10
Some other books that might be useful:

Quantum Mechanics in Simple Matrix Form by Thomas F. Jordan. A cheap dover. I think this is probably the simplest book out there apart the typical pop-sci word salad books.

Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles by Eisberg & Resnick. Does a good job with wave mechanics at an intermediate sophomore/junior level. Kinda pricey; look for it in the library or try to find a used copy.

It looks like MacMahon relied a lot on the QM book by Griffiths, which seems to be well liked on this forum (too pricey for me, though).
 
  • #11
Anthony Zee's 'Quantum Field Theory in a nut Shell', is a very good book as he gives motivation for a lot of the mathematics. It will start you off well, from which you can move onto something a bit more concise, but highly recommended.
 
  • #12
I think if he's still struggling with introductory QM, Zee will just sit on the shelf for quite a long time.
 
  • #13
Below is an excerpt from the preface of Griffiths, which is one of the more popular upper-division undergrad QM books. The Eisberg & Resnick book mentioned above would be more elementary and less mathematical.

Here's an older thread on this subject.
 

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  • #14
The book I recommended in the second post is:
P. A. M. Dirac: The Principles of Quantum Mechanics.

It has lot's of physics and clear explanations why we use the mathematics we use. Bit expensive on amazon, but I would believe not so bad as used. As they say "Learn from the masters, not from apprentices."
One good book focusing on the vector space side of QM is C. J. Isham's "Lectures on Quantum Theory: Mathematical and Structural Foundations". Paperback's cheap on amazon, very good for understanding, but doesn't teach you so much math.
 
  • #15
I was cheap and bought Schaum's Outlines Quantum Mechanics, and QM seemed hard.

Then I bought Griffith's Intro to Quantum Mechanics, and QM seems easy.

Schaum's is only good if you've already studied it and need to review before an exam - Griffith's textbook (for e&m also) is the proper way to go for truly learning the material.
 
  • #16
ChemGuy said:
I am using a "popular" book that has gotten poor reviews. It is by David McMahon. I think it got bad reviews because there are a million typo errors in it. I think it is making me look harder at each step in the solution. It does a pretty good job of explaining the steps but of course not perfect. I looked at Squires book but it doesn't look like there are any explanations. Is there or is it just a problems book.

If you don't mind, what is your motivation for getting back into QM? Is your background (math wise) similar to mine?

I am teaching Quantum Mechanics at the undergraduate level and, given your background, I would hughly recommend (as others did) that you get Griffiths. It's an excellent book for self-study. People have also suggested Eisberg and Resnick which is an excellent complement at a slighlty more basic level but more extensive in the topics covered (includes some nuclear physics, atomic physics, particle physics, etc). Then Schaum and McMahon can be good to practice a bit. But you definitely should go through Griffiths (Shankar is also excellent).
 
  • #17
My choice would be Shankar. He wrote his book to be self-contained enough for self-study. And it's cheaper than Griffiths, which seems to have a rather inflated price. (Of course, if you have access to a good library, check them both out.)
 
  • #18
Theoretical Physics = Physics + Mathematics + Philosophy :biggrin:

The book I recommended :The Principles of Quantum Mechanics (P.A.M Dirac)

http://www.phys.uu.nl/~thooft/theorist.html" , by Gerard 't Hooft
 
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  • #19
This looks interesting

I just requested this book from my library; it looks interesting, may also do the trick. I'll post an update when it arrives:

Author McMahon, David (David M.)
Title Quantum mechanics demystified / David McMahon.

Publication Info. New York : McGraw-Hill, c2006.

Note "A self-teaching guide"--Cover.

Claims to be just what you're looking for. More info at:
http://www.quantumphysicshelp.com/quantum_physics.htm
 
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  • #20
bruce2g said:
I just requested this book from my library; it looks interesting, may also do the trick. I'll post an update when it arrives:

Author McMahon, David (David M.)
Title Quantum mechanics demystified / David McMahon.

That's the book the OP has, and which I suppose prompted his original post.
 
  • #21
The Shankar book is "Principles of Quantum Mechanics" (Hardcover) by Ramamurti Shankar, in case anyone is looking for it.

There's a cute review of several books at http://brneurosci.org/reviews/griffiths.html

He doesn't like Griffiths because the solutions to the problems are only available to instructors, so it's not too good for self-study.
 
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  • #23
Has anybody looked at https://www.amazon.com/dp/0674843924/?tag=pfamazon01-20? Hughes makes an interesting choice. In order to keep the explanation level down to high school algebra (and a little trig), he restricts himself almost entirely to the case of quantum spin 1/2 systems, and Hilbert spaces isomorphic to C2.

Given this he does a pretty complete exposition of the Hilbert Space/operator formalism with calculations. Quite a coup in my view, and I could see a student beginning on this while still in calculus, and going on the the problems of infinite dimensional linear algebra, and then full-bore quantum mechnics with a deeper understanding than one who comes to the subject with the normal lower division college mathe preparation.
 
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  • #24
I'll have to check that out. Books that manage to do useful stuff as simply as possible (without just making word salad) are as fascinating to me as the really advanced books.

In Schwinger's posthumous https://www.amazon.com/dp/3540414088/?tag=pfamazon01-20 book, he "derives" the rules of QM inductively using Stern-Gerlach type experiments. Not all of it works for me (I don't quite follow the way he works out some of the probability rules...if you say so Mr. Schwinger...), but it's fascinating.

His colleague, Englert, who edited Schwinger's notes for this book has his own QM books out now which claim to be elementary and seem to follow Schwinger closely.

Baym did something similar but much less ambitious with photon polarization in his Lectures on Quantum Mechanics.
 
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  • #25
selfAdjoint said:

Yes - it's a favourite of mine, although I haven't really looked at it in quite a while.

It won't teach anyone to be a quantum mechanic, but loads of other books: do this well; don't do well what Hughes does well.

Hughes has a great line in his preface.

Having thus outlined my program and declared my allegiances, I leave the reader to decide whether to proceed further, or to open another beer, or both.
 
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Related to Learning QM and the math required.

What is Quantum Mechanics (QM)?

Quantum Mechanics (QM) is a branch of physics that deals with the behavior of matter and energy at a very small scale, such as atoms and subatomic particles. It explains how particles interact with each other and the laws that govern their behavior.

Why is it important to learn QM and the math required?

Understanding QM and the math required is important because it is the foundation of modern physics and plays a crucial role in many technological advancements. It also helps us to better understand the behavior of matter and energy at a fundamental level.

What are the basic concepts of QM that one needs to understand?

Some of the basic concepts of QM include wave-particle duality, superposition, and uncertainty principle. It is also important to have a good understanding of linear algebra and calculus to comprehend these concepts.

What are the mathematical tools required to learn QM?

The mathematical tools required to learn QM include linear algebra, calculus, differential equations, and complex numbers. These tools are used to represent and manipulate the equations and concepts of QM.

Is it necessary to have a strong background in math to learn QM?

While having a strong background in math can be helpful, it is not necessary to learn QM. With dedication and practice, anyone can understand the fundamental principles of QM and the math required to apply them.

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