Going to Tackle Griffiths E&M and QM: what math?

[Saladsamurai]

It has been awhile since my multivariable calculus course. I do not want to review everything before tackling these texts, just the important stuff.

What concepts and theorems are most important? Anything from linear algebra I should review?

Thanks.

 

[Feldoh]

I'm taking a class that's using Griffiths QM next semester and it looks like chapter 3 is in part linear algebra. At first glimpse you might want to look up Hermite polynomials, and series solutions to differential equations -- Or at least that's what I'm doing XD

 

[diazona]

For quantum mechanics, linear algebra will be fairly important - you'll need to be very familiar with vector spaces, orthonormal bases, and the principle of superposition, especially how any element of a vector space can be expressed as a linear superposition of the basis elements. This is because when you solve the Schrödinger equation, you find the independent "basis solutions" (same as with any differential equation) and then combine them to get actual solutions that fit some specific set of conditions. For what it's worth, I've had several years' experience with this stuff and I'm still getting used to it, so don't expect to completely understand all the linear algebra you will need - and be able to apply it - overnight ;-)

E&M is rather different; linear algebra is not so important, but vector calculus is. You'd need to be very familiar with the vector identities listed on the inside front cover of the book, and the various coordinate systems listed on the inside back cover (well, Cartesian, cylindrical, and spherical - they're pretty standard); also things like Stokes' theorem and the divergence theorem. Be sure you're comfortable with doing line integrals, surface integrals, and volume integrals in 3D space.

To some extent, the math can be learned along the way (Griffiths does a fairly nice job of explaining the math that goes with the physics), but I think trying to go through either book without at least having seen the stuff beforehand would be a waste of your time.

 

[gregarob]

I have been using both books for a while now. Be sure to look over the appendix of QM before proceeding at all. Refer to Chapter 3 if you are curious about some of the more formal math in the two preceding chapters.

Griffiths EM is one of my favorite books of all time. You will need to be very familiar with multivariable calculus, so be sure to brush up on it. If you are not too comfortable with curvilinear transformations, the appendix does a great job with it.

Enjoy!

 

[ice109]

i third that. know your vector calc integral type stuff like the back of your hand for EM.

for QM there's no hope. the math in that book is so sloppy and all over the place. I know all the linear algebra "required" for that book like the back of my hand and i still have no clue what he's talking about most of the time. learn how to do gamma integrals but that won't be useful till the last couple of chapters. you don't really need to know how to do anything because you're rarely asked to solve a problem from scratch. mostly it's just reapply the presented solution techniques with a whole lot of annoying algebra thrown in.

 

[Saladsamurai]

i third that. know your vector calc integral type stuff like the back of your hand for EM.

for QM there's no hope. the math in that book is so sloppy and all over the place. I know all the linear algebra "required" for that book like the back of my hand and i still have no clue what he's talking about most of the time. learn how to do gamma integrals but that won't be useful till the last couple of chapters. you don't really need to know how to do anything because you're rarely asked to solve a problem from scratch. mostly it's just reapply the presented solution techniques with a whole lot of annoying algebra thrown in.

haha. This is encouraging This is self-study, so I am expecting to struggle through most of this and to be asking lots and lots of stupid little questions here on PF.

Guess I should just dive right in.

 

[AUMathTutor]

A little complex analysis would be good for both. Familiarity with complex numbers will save you headaches in QM and allow you to work magic when solving Laplace's equation.

Fourier series would be a good thing to know how to do as well. This is used in both texts.

The E&M book is 1.0232 x 10^10000 times better than the QM book. The QM book is *horrible*. If you like math, prepare to become very angry at some places in that book (the author even admits you should become angry... there's a footnote saying as much, and I agree with him). He says "I'll explain this later" and never does... he'll say "as previously explained", and never did.

And conventional mathematical notation is, apparently, a suggestion, as he regularly abuses it (or at least it seemed so; it's been a while since I saw the book). Horrible, horrible book. If you can repress your gag reflex, though, you'll get a lot of good physics clotting your brain after that class.

 

[diazona]

I beg to differ with the last couple of posters: Griffiths QM is my favorite textbook for quantum mechanics. I used it for a year of physics courses, when learning quantum mechanics for the first time, and it was spectacularly helpful. I've relied on it for a reference ever since.

I will agree that it's not terribly detailed - once you've gone through the book and learned the material once or twice, there's not much more you can get out of it, and it quickly becomes easy to ask questions which Griffiths doesn't answer. But I still think it's a great introductory text. (And most people I know who have also used the book hold the same opinion)

 

[naele]

OP, the MIT open courseware website has full video lectures for multivariable/vector calculus and linear algebra. I haven't looked at the multivariable videos, but the linear algebra one is quite excellent.

edit: In case you decide to review. There's also a full video course for differential equations that gets into complex numbers and might be helpful.

 

[ice109]

haha. This is encouraging This is self-study, so I am expecting to struggle through most of this and to be asking lots and lots of stupid little questions here on PF.

Guess I should just dive right in.

it's not a good book for self study. shankar's principles of qm is a better book i hear. also Cohen-Tannoudji, Claude. Quantum Mechanics is good

 

[diazona]

it's not a good book for self study. shankar's principles of qm is a better book i hear. also Cohen-Tannoudji, Claude. Quantum Mechanics is good

I'm using Cohen-Tannoudji's book for a class right now (finishing up a 1-year sequence) and, to put it bluntly, it sucks ;-) Okay, maybe that's not fair... I would say it's comprehensive at the expense of being comprehensible. It's very detailed, which is good if you're using it as a reference, but I typically have to read any given section 2 or 3 times just to figure out what they're talking about. I'd consider it "the Jackson of quantum" - a good book to have on your bookshelf, but definitely not one I'd want to learn from. Especially not in the context of self study.

 

[ice109]

I'm using Cohen-Tannoudji's book for a class right now (finishing up a 1-year sequence) and, to put it bluntly, it sucks ;-) Okay, maybe that's not fair... I would say it's comprehensive at the expense of being comprehensible. It's very detailed, which is good if you're using it as a reference, but I typically have to read any given section 2 or 3 times just to figure out what they're talking about. I'd consider it "the Jackson of quantum" - a good book to have on your bookshelf, but definitely not one I'd want to learn from. Especially not in the context of self study.

in a certain sense you have to interpret every text unless you're the guy that wrote it.

 

[j93]

Im going to agree with diazona . because
a) Cohen-Tannoudji is not an introductory level book
b) Its a bit too much about the details for any beginner its the size of a phone book.
c) Its usually used for advanced undergrad text or intro graduate text.

Its the equivalent of suggesting a HS student read Goldstein's to learn Mechanics.

Griffiths or Shankar are better for someone first pass at self-studying

 

[qspeechc]

Griffith's QM book has a particularly horrid discussion of operators and several other mathematical aspects are poorly treated in his book imo. Get a book to complement Griffiths, and together they would be nice. I used Bransden & Joachain and thought the were excellent together. I have since found Zettili's book, and I find it fantastic. QM from Griffiths requires you know linear algebra atleast.

Griffiths EM book does an OK job of covering vector calc, but it's more like a refresher for someone who's already learned the math. It would also help to learn ordinary differential equations, and some partial differential equations, if you have time for the last.

 

[ice109]

Im going to agree with diazona . because
a) Cohen-Tannoudji is not an introductory level book
b) Its a bit too much about the details for any beginner its the size of a phone book.
c) Its usually used for advanced undergrad text or intro graduate text.

Its the equivalent of suggesting a HS student read Goldstein's to learn Mechanics.

Griffiths or Shankar are better for someone first pass at self-studying

totally doable for high school students who've completed the calc sequence and seen odes