Hey, thanks for visiting my site. I’m Jakob Schwichtenberg.

If you have any questions or found some error here or in one of my books please do not hesitate to contact me.

My mail address is jakobschwich (at) gmail.com or alternatively just leave a comment here.

## In Short:

I’m a physicist and I try to write down things during my own learning process.

In some sense, one of the biggest benefits I have over other people in physics is that I’m certainly not the smartest guy! I usually can’t grasp complex issues very easily. So I have to break down complex ideas into smaller chunks to understand it myself. This means, whenever I describe something to others, everyone understands, because it’s broken down into such simple terms.

Moreover, I’m by no means an expert in the subjects I’m writing about and I believe this is another huge advantage.

All this is perfectly summarized in the following two quotes:

The first one is from C. S. Lewis

“It often happens that two schoolboys can solve difficulties in their work for one another better than the master can. […] The fellow-pupil can help more than the master because he knows less. The difficulty we want him to explain is one he has recently met. The expert met it so long ago he has forgotten. He sees the whole subject, by now, in a different light that he cannot conceive what is really troubling the pupil; he sees a dozen other difficulties which ought to be troubling him but aren’t.”

and the second one is loosely paraphrased from Donald Knuth

With my posts, I’m not trying to be on top of things. Rather I try to get to the bottom of things. I try to learn certain areas of physics exhaustively; then I try to digest that knowledge into a form that is accessible to people who don’t have time for such study.

## Longer:

“Everyone sooner or later invents his story which later becomes his life”– Max Frisch

So here’s mine

I was bad in school. Not so bad that I got into trouble, but still pretty bad. I was bored most of the time and only invested the minimal amount of time which was necessary to pass the exams. To give an example, in the 10th grade I got a 4, which is the German equivalent to an American D, in mathematics. This is exactly the grade you need to pass without getting into trouble.

A few years later I got mostly straight 1s in mathematics and started studying physics shortly after. To this day I spent most of my time thinking about mathematics and physics.

How did this change happen? How did I transform from a bad student into a passionately interested student with universally good grades?

This is what this story is about.

Looking back, I think my problem was that I never understood why I should care about the things the teacher talked about. While for many students getting good grades is motivation enough, this never worked for me. In some sense, I understood too early that grades don’t matter.

I remember asking my teachers several times, especially in mathematics, why we were taught certain topics. “What can we do with this? Why is this important?” I didn’t get satisfactory answers and was rewarded with bad oral grades.

Then something huge happened.

During this time I visited frequently flea markets with my parents. One day when I was 16 I bought at such a market a book titled Surely you’re joking Me Feynman. This was the best Euro I ever invested. This book turned my world upside down. Before reading it, I was mostly interested in computer games and soccer. But with Feynman’s help, I finally understood why people care about mathematics and physics. I started to understand that physics and mathematics aren’t the boring things, that the teacher presented. Instead, they are fun and important. In physics, you are trying to understand what makes nature tick at the most fundamental level. Mathematics is the language that you need to talk about physics. This was what I was craving all the time. I suddenly got interested in all those tricks that the math teacher presented because I was curious about how they can help to understand nature. Suddenly school was fun.

Needless to say, I was hooked afterward and read every book by Feynman I could get my hands on. Then every physics and mathematics book. I’m hooked to this day. However, there were few books that had such a big impact on me as this little book by Feynman.

A few years later I got really interested how this transformation happened. One day I was only interested in computer games and soccer, and only a few weeks later I was crazy about science and mathematics. In addition, all those things that didn’t make sense to me suddenly did.

My quest to understand this paved the way for the journey I’m still traveling.

Suddenly it was really easy to understand the things, for example, the math teacher talked about. What previously sounded like incomprehensible jibberish, was only a few weeks later completely logical and sensible stuff.

Needless to say, my grades got better. A lot.

What finally helped me to understand my own transformation, were two books:

- Psycho-Cybernetics by Maxwell Maltz (which I also bought at a flea market),
- Outliers by Malcolm Gladwell (which I bought on a street market in Mumbai).

The main point I took from these two books, which I believe to this day, is that there is no such things as talent or intelligence.

While you can, of course, define these two words however you like, the important thing is that they aren’t useful concepts in any way.

Intelligence is what is measured by an intelligence test. You can train the riddles that you need to solve in an IQ test and this way you can increase your IQ. Is this meaningful? Of course not. This only means that you got better at solving these kinds of riddles and nothing else. There is no correlation between what is measured in an IQ test and any type of success in life. The biggest discoveries in science aren’t made by the smartest guys.

Talent is similar, but even more ominous, because there isn’t even a quantifiable notion like the IQ for intelligence.

So why are these notions so popular nevertheless? Because they are convenient. On the one hand, they are convenient to excuse why you aren’t able to do certain things.

“Well, I simply have no talent for mathematics.”

“I’m not smart enough.”

On the other hand, they are used to feel better than other people. Haha, look at these dumb people. Us vs. Them mentality is always powerful.

I would like to go even further and say that they are not only useless but actually harmful.

Most people never reach their potential, because they think they don’t have what it takes. This is incredibly harmful bullshit. As long as your body and brains work reasonably good, you can achieve whatever you want.

It makes actually no sense to believe in intelligence and talent. Even if I’m wrong and there is such a thing, talking and thinking will only have the effect that you start doubting and limiting yourself.

In addition, I learned from Maltz and Gladwell that the only things that matter are your self-image and motivation.

By reading Feynman’s little book I started to get interested in science. I got curious and motivated.

In addition, it transformed my self-image dramatically. Feynman’s IQ was only 125. Nevertheless, he was one of the most important scientists of the last century.

Motivated and with a transformed self-image I was as smart as the smartest guys and girls in my class.

To this day I’m convinced that everyone can understand any topic if he is sufficiently curious about it and reads an explanation that speaks a language he understands.

This is what motivates me to write.

A few words to say your book is really well written and clear from a self learner in physics. Good work to explain some advanced concepts without need at the beginning of advanced mathematical topics. Thanks

Nicolas

I thought I had already hit a ‘ceiling’ in learning physics after struggling through my undergrad classes. It partly had to do with an inefficient and ineffective way of learning the subject, resulting in a general anxiety towards approaching more ‘advanced’ topics (i.e. the Intro EM and QM classes were already daunting experiences at that time).

But after graduation, I decided to give it a second shot. I began by watching youtube physics tutorials and lectures, picked up the standard undergrad textbooks again, and read them carefully. Things became less vague, my knowledge gaps slowly closed, and the pieces of the puzzle started to emerge. I stumbled upon your book on Amazon, got an e-copy (legally) and wow, I am surprised I’ve been following it for more than 130 pages (of course, having checked the errata along the way). Your explanation, derivations and logic helped me fill even more knowledge gaps, link ideas that seemed irrelevant and allowed me to appreciate the beauty of nature even with such limited background knowledge.

Thank you very much Jakob for the book. I whole-heartedly agree that a lot of experts forget what it’s like to be a beginner. Even for those authors (like Griffiths) who could explain things very well to a beginner, those I’ve encountered so far only cover one topic at a time (EM, QM, Classical Mechanics, etc.) and it is so hard to be ‘revealed’ the ‘higher level’ connections and intuitions from a top-down level. I really appreciate your effort to cater to ambitious beginners / amateurs like me who didn’t go through the grad school journey to discover how things ultimately work. Whether this becomes an undergrad ‘standard’ text or not, I believe you put in all these effort not for the money or fame, but out of a compassionate heart who want to help the strongly curious, but clueless, folks to actually ‘get there’. Thanks again.

I’m a process chemist, so I haven’t looked at general physics in quite a while, and I haven’t finished this book yet, but what I have read is superb. I never like giving students formulas simply to memorize, and as good as some books are, they all seem to invariably partition the subjects that they try to teach, which makes integrating the knowledge into their web of knowledge and internalizing it a much harder task for the students. Einstein may have said that if you can’t explain something simply, then you don’t know it enough, but it would help if textbooks, and not just students and teachers, would strive for that goal. This book does it far better than any book I have read (though again, I haven’t read one recently). Thanks for producing it.

Have you thought about contacting a company like the Great Courses, and maybe trying to teach a general physics course with this approach? It seems like the style of learning they are interested in, and they don’t shy away from difficult concepts, as seen in the Superstring Theory lecture series. Might be worth a look.

Thanks again.

Edward

Hi Jakob,

cool that you have already written such a book while still being a student, both thumbs up ;-)!

I will probably read it in German.

At what university are you?

Best wishes

Dilaton

Hi Dilaton,

thanks!

I’m currently a PhD student at the KIT.

Best wishes,

Jakob

PS: I’m a huge fan of your PhysicsOverflow project!

Hi Jakob,

thanks for the nice words about PhysicsOverflow !

Cool place to be where you are and you seem to be doing cool stuff 😉

BTW I will have the pleasure to write a few words (aka Rezension) in the German magazine “Physik in unserer Zeit” … 😉

http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-3943

Cheers !

What’s KIT? I’m not German, so I am not acquainted with the educational institutions.

KIT = Karlsruhe Institute of Technology

Hi Jacob and thanks for a great book !!

Could You please explain for me the math. behind Eq. 3.94 and 3.105

Sinc. Trond Braaten

Hi Jakob,

Thanks for your book. It was really awesome. This book helped me to understand Group theory and High energy physics.

I’m so happy to be reading this. You are amazing. Finally someone says things out loud that were always in my brain! Thank you. 🙂

Thank you so much for sharing and writing this and your own book! They’re both really encouraging and helpful! Thank you so much for what you’re doing! You’re a strong, wonderful person!

Hi Jakob, I just bought your book “from finance” – looking forward to reading it. Drop me your contact please. k

Hi Kirill,

you can reach me at jakobschwich (at) gmail.com

Best wishes,

Jakob

A beautiful note, thank you, Jacob. We are all inspired by Feynman in some way I guess. I struggled with math in high school and college. I took an easier path and majored in Economics. I “regretted” that choice over Physics. Thank you for your books. They are good place to start for self-study amateurs. Can we become Facebook friends? I am from Hong Kong.

I am unclear what exactly ! over = means. Otherwise greatly enjoying Physics from Symmetry

Hi,

an equals sign ‘=’ with an exclamation point ‘!’ above it means „should be“ or „we want it to be“ .

A technical question about your blog: How do you write your latex formulas? The standard Worpress using creates pictures, but in your site the formulas consist of sepatate characters. (I make a try, $\frac{a}{b}$. Will it work?) How does it work?

The LaTeX formulas on this site are rendered using Mathjax (https://www.mathjax.org/).

Hello Jakob. I’m a second year engineering student in Denmark and one of my courses has your book, “No-Nonsense Electrodynamics” from 2018 second on the recommended reading list.

I was wondering if you could help me get a copy of the e-book, since I can’t afford getting a digital copy from Amazon or other listings. I would be very grateful if you can contact me back on this subject.

Hi Zoltan,

I’ve sent you an email!

Best,

Jakob

I don’t know if what you say is true of false, but I believe it enough to buy your book.

Hi Jakob, I’m a third year physics undergraduate interested in self-learning group / group representation theory. Your two essays “How is a Lie Algebra able to describe a Group?” and “What’s so special about the adjoint representation of a Lie group?” helped clear up some of my conceptual gaps left by other internet resources and actually allowed me to start using group theory explicitly in my linear algebra and quantum mechanics homework. What textbook would you recommend I use for more rigorous study of the topic?

My favorites are Naive Lie Theory by Stillwell and An Introduction to Tensors and Group Theory for Physicists by Jeevanjee

Hi – I have a question about your Quantum Field Theory book.

I think eqn 6.12 should have a phi_0 added on at the end, where phi_0 is the solution of the free Klein-Gordon equation. Doing this doesn’t affect eqn 6.11 since operating on phi_0 with the K-G operator just gives 0 anyway. In this sense, phi_0 acts like a ‘constant of integration’ in calculus.

The problem is that later when you discuss perturbation expansions in interacting fields, some of the equations don’t seem to be correct.

For example, in eqn 6.28, if lambda=0 (no interaction), this equation says that the field phi is just 0, rather than the free field phi_0.

Again, in eqn 6.32, equating coefficients of powers of lambda would lead us to conclude that phi_0 = 0, since there is no term on the RHS with lambda^0.

Similar problems crop up in section 6.3 in discussing Yukawa interactions, where equating coefficients of powers of g in eqn 6.41 leads to phi_0 = 0 and in eqn 6.54 would lead to psi_0 = 0, rather than giving the free field in each case.

Thanks.

Yes, you’re right! Thanks for reporting this issue. I will fix it in the next version of the book.

Jacob,

I’m working through “No-Nonsense Quantum Field Theory”, and I love the book and your approach. I may have found a little typo (a dropped “-” in 2.49, p. 63). No worries, all but inevitable in a text like this. Are you collecting these? Is there a better way to forward any if I find more?

Thanks again, a great book!

Glenn

This is me, replying to my own comment: So sorry! I know it is Jakob. My typing just got away from me! Thanks!

Thanks Glenn! I update the book regularly to and the best way is to send them to me via email: [email protected].

Best,

Jakob

Hey Jakob, I’m reading your book Physics From Symmetry, It’s really interesting! I’m on chapter 4 and I haven’t been able to put it down!

Dear Dr. Schwichtenberg

I am an accomplished plasma and particle accelerator experimental physicist. I have wanted to know the basis of the Standard Model of particle physics, but was defeated in all my attempts over 3 years because of my lack of preparation in Group Theory and Abstract Algebra. I had been spending many hopeless hours in understanding this mathematics.

Then I stumbled across your book on Symmetry. It is exactly the thing I needed to link my physics knowledge to the branch of Algebra. It is one applied physicists and engineers and other students would learn from. It is practically perfect and I am learning a lot. I am very grateful to you for making this available to us.

I wish you all success in your pursuits and work. I hope I can write to you requesting any clarifications.

Sure, I’d be happy to help!

I never did my Ph.D. discertation in Control Systems Engineering due to personal life issues, but have pursued my passion for teaching at a community college. I left industry after working as an Electrical Engineer for 25 years, and have always been interested in physics and your books (I purchased every one) are “filling-in” the bigger picture for me. I truly enjoy your writing style and approach. Thank you so much for providing your insight to the subject matter.