This blog will provide tutorial articles on various topics in serious science. Curious but cautious readers may be interested in what to expect, so here are a few guidelines:

- I’m aiming at people who want something a bit more substantial than the popular science market, so, yes, there
*will*be some (in some cases, a lot of) equations. The level of math that I assume varies, but in general I assume a good grounding in calculus, algebra, matrices and vectors. **An index to the posts is provided – see the index links on the right.**- If you’re looking for my notes on a specific chapter of one of the books that I’m working on, try searching for the author’s name, a keyword from the title and the chapter you’re interested in. For example, you can search for Griffiths Quantum “Chapter 4” (including the quotes around “Chapter 4”) to get my notes from Griffiths’s
*Introduction to Quantum Mechanics*, Chapter 4. - I don’t provide separate downloadable versions (such as PDFs). There are a couple of main reasons for this. First, it would take a lot of time to create these PDFs for the 1600+ posts (I don’t know of any automated way of doing this, since I would need to export each post in the LyX editor, upload the files and provide links to each of them). Second, if I correct errors (which many readers have kindly pointed out), I’d need to update the PDF as well as the web page. Finally, it
*is*possible to download a page (at least in Chrome and Firefox, I don’t know about other browsers) to read off-line. In Chrome or Firefox, right-click anywhere in the text (not in an equation) on the page, select “Save as…” and then in the Save dialog, select “Web Page, Complete” as the “Save as type”. This will download the page and include all the images (the equations are all images generated by WordPress) into an HTML file and sub-folder for the images which you can read off-line using Chrome or Firefox. **The easiest way to keep up to date with new posts and comments is to subscribe to the RSS feeds or for email updates (see links on lower right).**- Mathematics is written using WordPress’s Latex feature. Latex can also be used in comments. Although Latex can be used to write entire books, it is only the mathematical typesetting features that are used here. For example, the quadratic formula can be written in Latex as . There are many web pages dealing with Latex, but a good introduction is here, where you should look only at the bits on mathematics.
- Pages containing a lot of mathematics were written entirely in Latex using the LyX editor and then converted to WordPress format using the Python program
*Latex2wp.*I’ve made a few modifications to the original Latex2wp program so that it displays equations better. - If you’re having difficulty reading some of the smaller fonts (e.g. superscripts and subscripts) in the equations and aren’t viewing the page on a touch sensitive screen that supports pinch-zoom, just use your browser’s zoom function to enlarge the page. For Chrome, you can zoom in using [ctrl][shift]+ and zoom out using [ctrl]- . Other browsers no doubt have zoom functions as well – look it up in their documentation or use Google.
- Feynman diagrams were produced by the JaxoDraw program.
- These blogs are a result of my working through several textbooks on various aspects of physics and mathematics. The pages are essentially my own notes that I took when reading these books. A list of the books I’ve used is given on the References page (see the References link in the Index menu above), and the specific section of the book used in each post is referenced at the top of the post. Although this blog tries to provide self-contained summaries of topics (with crosslinks to other pages for background where necessary), there is no substitute for a good, coherent coverage of a complex topic so I’d strongly advise getting hold of these books, or ones like them, if you want to study a subject in depth.
**Finally, if you’re looking for solutions to problems, PLEASE PLEASE make a genuine effort at solving the problem yourself before looking up the answer (on any web site). You’ll learn very little by just reading the solution without trying to solve it yourself first, and if you’re taking a course, you will need to understand the material properly to stand a chance of passing the exams. Remember that in most universities, the exam counts for half or more than half of the credit for the course.**

If you have any suggestions for topics to include, or any other comments or criticisms, please do leave a comment to this message.

The photo in the header of physicspages.com was taken by me at Glen Doll, Scotland. I was lucky to be there when the cliché rainbow appeared.

growescienceI haven’t got that far into Schroeder’s book yet, but from what I’ve read, his writing style is similar to that of Griffiths (informal, with good explanations and derivations). A while ago I asked for recommendations on my blog for a stat mech book and Schroeder was the one that most people recommended, so it seems to be fairly standard. The other main book is the one by Pathria, but this is (I think) at a more advanced level, so if you’re just getting into stat mech, Schroeder is probably your best bet.

As for classical mechanics, I don’t really know as I haven’t studied it myself since my student days back in the 1970s. Back then, the standard text was the one by Goldstein, which is written in a more formal style. I’ve heard Taylor’s book mentioned but I haven’t read it so I can’t say how it compares to Griffiths.

Patrick DennisI’ve read that editors warn would-be popular science writers that they stand to lose 10% of their readership with every equation. Most seem to believe it.

But there are some of us who had, say calculus I & II in college, along with a year or two of (calculus-based) physics before moving on, and who actually enjoyed those subjects!

Truth to tell, however, it seems that calculus gets you up to maybe the beginning of the nineteenth century when it comes to understanding the things physicists think, speak and write about. Beyond F = mdv/dt, there’s not much out there for the non math-phobic layman, but your blog seems willing to “go there,” so I consider it to be a real find!

I’d guess that your discussion of integration is leading towards Lagrangian mechanics, not covered in my undergraduate physics courses, so I’ll be following with interest. (Can differential geometry and group theory be far behind?)

growescienceThanks for the encouragement. I’ve been looking for a retirement project and I had my doubts as to whether a full exposure to mathematics would have any audience, so it’s good to know there are some people out there who would appreciate it.

As for calculus, though, I think you’re being a bit pessimistic about its applicability to physics. I’d say a knowledge of calculus (together with vectors and linear algebra) would take you well into the 20th century, and would certainly cover all of the 19th century. All of electromagnetism and statistical mechanics, as well as most of special relativity and non-relativistic quantum mechanics need only that level of math. It’s really only when you get into general relativity and high energy physics that you need something more.

Anyway, thanks again and please do continue to post comments to let me know if anything is unclear or if there are pet topics you’d like me to post on.

gert korthofHi Glenn,

I found your page

http://glennrowe.net/BaronCohen/EmpathyQuotient/EmpathyQuotient.aspx

when searching for Simon Baron-Cohen’s EQ test which I found in his book The Science of Evil (2011). I noticed it was different from the one on your website. The book version has a adult and a child version. Have you seen this? Are you planning to add these EQ tests to your website?

Gert Korthof

growescienceI’m afraid I haven’t kept up with Baron-Cohen’s work, so I haven’t seen his latest book. The tests on my web site are taken from his earlier book “The Essential Difference”. I don’t have any immediate plans to add anything to the site but might eventually get round to it.

gert korthofThanks Glenn.

I am impressed with the huge number of participants (>314.000 is that right?) of your EQ test! That is really impressive, probably a scientific experiment no scientist in the empathy field has ever done. Congratulations!

I can send you the text of the new EQ tests if you are interested in making a new online test (modifying questions of the old test does not work of course).

By the way I enjoyed his new book very much, I don’t know his previous book. Especially I found it very useful and interesting to do the EQ test in his book, but is was on paper and searched for an online version, which would be even more fun to do. That’s how I came across your website.

Have a nice day,

Gert

growescienceYes I am surprised at the continuing popularity

of the page – it’s been up for many years now and it still gets several hundred hits every week. I’m not sure it would qualify as a scientific experiment since I have no idea how many people are telling the truth, but the results do seem to support the statements in Baron-Cohen’s original book – male brains are better at logical things and female brains are better at empathic things.

I think I’ll leave the site as it is for now, but I might have a look at his new book.

Thanks for your interest.

imanrealy realy realy thank you man!!

you rock!equations and math?they are the joy of physics!!I love them.I live for them!actually I dont like physics.nor math.I love MathematicalPhysics.

Isnt it fun to work and explore orthonormal polynomials?Hillbert spaces?ladder operators?

Sir could you introduce yourself a bit?

you have my deep gratitude!

Im iman.17.I study physics and math.

I will be glad to help you with this nice and great blog.

iman

growescienceI’ve got a personal web page at http://glennrowe.net if you want a bit of info about me.

Thanks for the offer of help on the blog, but it’s just a hobby with me so I think I’ll carry on by myself. However, if you want to start your own blog, it’s easy enough – just sign up with wordpress.com (it’s free unless you want a dedicated URL). To put in equations, though, you’ll need to know some Latex (see links in the intro at the top).

imanthank you.

I saw your personal webpage.

I love the way you think!or precisley I like the way I presume you think!

you are waaay older and experienced than me though and I am reaaaallly glad I found your blog!!

secondly:could you make a place in your blog for people to post their questions or can we post them here?for example I have a problem concerning dielectrics:

we have a capacitor with a dielectric in it.what are the charges on the surfaces of the capacitor?

and once again thank you sir.realy realy thank you.

it is so nice of you to run this blog.and hell…I thought you might be 20 or 30 years old!!why are you retired??why dont you teach,write or research anymore??you ARE awesome and you dont look old a bit!!

two thumbs up!!you ROCK man.

imanproblem:

charge on a conducting needle??

we want to find the charge density.

I have solved it using the problem of charge on an ellipsoid then taking the limit as the ellipsoid tends to a needle…but I want to solve it using laplace directly or by a mathematical solution>>we need a charge density F so that the potential is constant on the needle.

please answer this.thank you.

growescienceIt seems as though there might not be any known answer to this. I don’t have this paper, but from the abstract, that’s what Griffiths says: http://adsabs.harvard.edu/abs/1996AmJPh..64..706G

Anonymousmy answer actually works..i mean it should work!!

you can find the answer for an elipsoid on Smythe ‘s book on electricity and magnetism ..Then you take the needle to be a limit of ellipsoid.it quite works!

but Griffiths has tested experiement and numerical data…which the test is WRONG according to Jackson.which later Griffiths himself accepted he was wrong.

G. Binnig, H. Roher, Scientific American, Vol.253, Aug. 1985, pp. 50-56

C. F. Quate, Physics Today, Vol. 39, Aug. 1986, pp. 26-33

D. Griffiths, Y. Le, “Charge Density on a Conducting Needle�?, Am. J. Phys. 64, 706-714, 1996

J. D. Jackson, “Charge Density on Thin Straight Wire, revisited�?, Am. J. Phys. 68, 789-799, 2000

D. Griffiths, O. F. de Alcantra Bonfim, “Comment on ‘Charge Density on Thin Straight Wire,

Revisited’, by J. D. Jackson, Am. J. Phys. 68, 789-799, 2000�?, Am. J. Phys. 69, 515-516, 2001

imanhere is a nice question:

we have two q charges with distance 2a apart.

now on a line perpendicular to them and from their center we want to place a third charge(also q).in the diagram x’s are the line.

q–O–q

x

x

x

x

q

if we name the distance between the third q and the center of the q’s(O) “L”

for some L we have two points between O and the third q that the field is zero.

for only on L we have one.

and for some we have none.

find the L which we have only one point where field is zero amidst them.

and sketch the field lines.

imanthose x’s and the third q where supposed to be joining O!!

imanwhat is an image charge inside a cylinder?

aaronsmith07Hi Glenn,

Thought I’d leave you a message to thank you for taking the time to do this blog. I am certainly glad the spirit of your blog is to provide a resource for those who dare to find out about this thing we call nature without superficiality. I say dare (for ranty reason on my part for which you must forgive me) because, although I have spent a short time on this planet, I know of few people who have taken on an academic subject as a hobby apart from myself much to my dismay. So again, I thank you.

I switch between you and griffiths electrodynamics for different but similar takes on explanations and respective solutions to the questions. For which I believe you make things more obvious than griffiths at times, the little things definitely. Just been reading about electrostatic pressure which highlights my point I think.

Was just looking through your website and was surprised to see you reside in the same country as myself(What made you choose Scotland?!). I’m currently at Aberdeen in my final year of medicine (starting mid august!). Although I dabble from developmental biology and evolution(for which I hold a degree in) to physical chemistry, physics particularly electromagnetism at the minute when I can. I’ve also dabbled myself in Russian plus other languages throughout the years ever since I was a kid, I still find cyrillic writing beautiful but alas to do not remember much of the little Russian I once knew. Also a lover of art particularly impressionism and 1920 surrealists if any of that kicks your boat and history myself. It annoys and embarrasses me how little I know of history. I’m also musical myself although I have been playing a very long time so I’d like to think I’m not too bad.

Hope your endeavours go well and hope you continue your blog.

Kind regards.

growescienceHi Aaron – thanks for the kind words. I started the blog after retirement since although I did my degrees in physics I never had a chance to use it much in the career that followed, so I thought it would be good to relearn what I once knew. If I live long enough I’d like to get far enough to understand all the fuss about the Higgs boson, but that could be a while yet.

I find Griffiths’s textbooks to be so good that a lot of the time it’s hard to find another way of explaining things that is any better than his, but as you say there are a few small things that he skates over so I’ve tried to expand on those. I wish he’d write some books on other areas of physics but judging from the detail and number of problems in his existing books I imagine that would be no small task.

I moved to Scotland basically because there was a decent job here after I finished my PhD in Toronto. I have to say it’s a more pleasant place than Toronto, at least as regards the weather (local Scots will probably find this surprising, but I got sick of Toronto’s freezing winters and boiling summers quite quickly).

I too have forgotten most of the Russian I once knew, although I still remember the alphabet so I can pronounce Russian words even if I don’t know what they mean.

imanhi…recently you dont write so much …

please write more…!!

thank you.

SeshuYour blog is wonderful…Thank you…It really helps for physics loving people like me 🙂 I have one question…is there any solid mathematical treatment for the fact that an accelerated charged particle will lose energy by radiation? I could not find, if you have, please post it or mail me.

growescienceI’m sure this is part of classical electrodynamics, but I haven’t reached that far myself so I can’t help you yet.

SeshuIts ok..

Chan HangDear Sir,

Thank you for this wonderful page. The solution provided really help alot in my learning. I would like to take this opportunity to seek advice for my self-studying in Physics. I am an engineer with Bachelor Degree in Mechanical Engineering. Even though I have already graduated, because of my keen interest in Physics, I still self-studying in Physics everyday little by little. I know that the three core subjects of Physics are Classical Mechanics, Classical Electrodynamics and Quantum Mechanics. For Mathematics, I use “mathematical methods in the physical sciences, Boas” and for Quantum Mechanics, I use “Introduction to Quantum Mechanics , griffith”. I would like to ask beside master in these three subjects, what else should I focus to enchance my Physics level and how should I carry out my study plan? Awaiting for your kind advice. Many thanks. =)

growescienceI’m not an expert in the area, since the last time I did physics in a university was about 30 years ago and I’m just relearning a lot of the stuff I did back then. I would add a few other core subjects to your list, however. First, there is relativity; special relativity is essential, although general relativity (Einstein’s theory of gravity) is useful if you want to study astrophysics or cosmology. Statistical mechanics and thermodynamics are also fairly ‘core’ subjects.

For electrodynamics, Griffiths’s textbook

Introduction to Electrodynamicsis excellent (and is one for which I’m posting my solutions). I haven’t looked at special relativity books for a while so I can’t recommend anything there, but Moore’s bookA General Relativity Workbookis a simpler introduction to general relativity than most other books. I don’t know what the currently popular textbooks on statistical mechanics are either, but perhaps someone else will post something.Keep on learning; it’s always enjoyable and rewarding.

Chan HangThanks for your kind reply and precious advice. Looking forward for your new topics and tutorial ! =)

Chris KranenbergHello Glenn,

Thank you for taking the time providing solutions to Moore’s General Relativity Workbook. I’m using the book as a self-study guide and your solutions provide valuable feedback. As an aside, I have posted solutions to Keith Symon’s 3rd Edition Mechanics and part of Taylor’s Classical Mechanics as resources for those students addressing upper level undergraduate classical mechanics. So, I can relate with your passion of sharing solution methods for the benefit of physics students and enthusiasts.

jose ignacioHi, where can i found the solutions to Keith Symon’s 3rd Edition Mechanics?

karulgI really like the Griffiths books, as a beginner lecture to find get into the topics. Can you recommend any similar books for the other 2 standard theoretical physics courses (calssical mechanics and thermal physics)?

For mechanics i was thinking about Taylor. For statistical/thermal i have no clue. Is the Schroeder – Thermal Physics (found on your page) similiar to Griffiths?

growescienceI haven’t got that far into Schroeder’s book yet, but from what I’ve read, his writing style is similar to that of Griffiths (informal, with good explanations and derivations). A while ago I asked for recommendations on my blog for a stat mech book and Schroeder was the one that most people recommended, so it seems to be fairly standard. The other main book is the one by Pathria, but this is (I think) at a more advanced level, so if you’re just getting into stat mech, Schroeder is probably your best bet.

As for classical mechanics, I don’t really know as I haven’t studied it myself since my student days back in the 1970s. Back then, the standard text was the one by Goldstein, which is written in a more formal style. I’ve heard Taylor’s book mentioned but I haven’t read it so I can’t say how it compares to Griffiths.

alexWould say its similar in clarity. Its better than the usual options for undergrad mechanics (like marion thorton). I’ve haven’t use taylor in a while, so I would be biased in saying that I like griffiths better at the moment, but can definitely say I enjoyed reading through it while taking mechanics

ibkevI am embarking on my own self study in physics (having graduated from engineering back in 1992.) In the process of coming up with a study program, I came across your blog and am finding it so inspiring that I’m going to give blogging-as-I-go a try now too!!

One thing I’d be curious to hear your opinion on is something that I’ve discovered recently called Geometric Algebra. Are you familiar with this? It seems complex variables, vectors, quaternions, matrix theory, differential forms, tensor calculus, spinors, twistors, are all unified by geometric algebra, leading to surprising results like Maxwell’s 4 equations becoming a single equation when described by it and the suggestion that the Dirac equation contains additional information when viewed geometrically.

This guy from Cambridge’s astrophysics dept talks about it here:

http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/03/oxford_undergrad_physics_conf_april_2008.pdf

Also, this

http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/ImagNumbersArentReal.pdf

gwrowePost authorI’m glad you find the blog inspiring 🙂

I haven’t heard of geometric algebra but I’ll have a look when I get a chance. Thanks for the references.

marcusReally well laid out blog, I’ve just started my first QM course with the OU as part of my undergraduate degree , and look forward to spending some time reading thru your work here. Thanks

StringTheoryDear Dr Rowe,

Thanks for making this site.

See if you are interested in this book:

A First Course in String Theory, 2nd Edition: Barton Zwiebach

In case later on, you are also interested in this book, you are welcome to discuss with me the exercises, although I have only finished the first half of the book.

gwrowePost authorI bought this book a while back but haven’t had a chance to look at it yet. However, if it’s as clear as Zwiebach’s lectures it should be a good book.