Quantum Mechanics and Relativity Journey

[ajassat]

I am interested in Quantum Mechanics and relativity. Because I am only fifteen I am unable to understand everything fully - however I usually get the main ideas and can understand the mathematics (unless it is very abstract - like matrix maths).

Everyday when I decide to read something about QM or Relativity on wikipedia I am bombarded with so many different phenomena and principles. I searched Quantum Mechanics, and then I sidetracked to the Photoelectic Effect, Superposition and Entanglement. Often this leads me very confused.

I would like to know in which order I should read/study Quantum Mechanics. Which order of study/gaining knowledge will make sure I don't get confused. A comprehensive order would be good - including the Maths I need to learn in between too...

If anybody has good links related to the area, then post them too. I really want to get a grip on QM and relativity - it excites me a lot.

Adam

 

[Monocles]

Wikipedia isn't a good reference to learn the material. Most technical articles are designed for people who already have a good understanding of the topic. I recommend checking out the Math and Science Learning Materials section of these forums, and also iTunes U (its part of the iTunes music store, but its just a bunch of video lectures you can download for free).

 

[Riogho]

The best thing you can do, since you are 15, is read layman books. The math will most likely be beyond you, and layman books do a good job in presenting the information so you (and I) can understand it.

Coming from a fellow Adam, and one who was interested in Relativity and QM at age 15, I have a few good books to reccomend.

For relativity the best one I've found is "Black Holes and Time Warps: Einstein's Outrageous Legacy" by Kip S. Thorne

For QM if you're interested in the history get "The God Particle" by Leon Lederman, if you want to get straight to the meat try "The Theory of Almost Everything" by Robert Oerter.

Enjoy :D

 

[neworder1]

IMHO the best thing you can do at your level is to learn all prerequisite math first. If you have mastered precalculus/high school math, the next step is calculus and linear algebra. Thorough understanding of these topics is absolutely necessary if you want to learn real stuff, not only popular science (trust me, matrix algebra is one of the least abstract things you'll encounter). Of course it depends on how much you already know, but learning necessary math can and probably will take a lot of time, and sometimes be tedious. However, there is no other way.

Also, you'll greatly benefit from general physics background - quantum mechanics is an advanced topic, so make sure you have learned your high school physics, and then move to introductory college-level textboks, e.g. Feynman's lectures. Quantum Mechanics is usually taught at university around 2nd-3rd year, because students need to learn necessary mathematics and physics backgroud fist, and that takes approximately two years.

 

[ajassat]

Thank you for responding to my question. I have thought about buying some layman books and I have no more questions regarding this.

I still have some issues to clarify in regards to information given by 'neworder'. I have mastered high school math (solving quadratics, trigonometry, proportionality etc...). When you mention calculus and linear algebra do you know any good links where I could start from? Also, is there any introductions to linear algebra? Finally that comes after this?

Thanks in advance.
Adan

IMHO the best thing you can do at your level is to learn all prerequisite math first. If you have mastered precalculus/high school math, the next step is calculus and linear algebra. Thorough understanding of these topics is absolutely necessary if you want to learn real stuff, not only popular science (trust me, matrix algebra is one of the least abstract things you'll encounter). Of course it depends on how much you already know, but learning necessary math can and probably will take a lot of time, and sometimes be tedious. However, there is no other way.

Also, you'll greatly benefit from general physics background - quantum mechanics is an advanced topic, so make sure you have learned your high school physics, and then move to introductory college-level textboks, e.g. Feynman's lectures. Quantum Mechanics is usually taught at university around 2nd-3rd year, because students need to learn necessary mathematics and physics backgroud fist, and that takes approximately two years.

 

[neworder1]

As for good textbooks on calculus and linear algebra, browse this forum and you'll find a plenty of links and material. For example, try searching here: https://www.physicsforums.com/showthread.php?t=122924"

You should get some good textbooks, it's not a good idea to learn solely from Wikipedia/other net sources.

 

[Fearless]

The maths

- calculus in one and several variables (Here I think that you should've learned differential equations)

- linear algebra

- complex analysis

- Fourier analysis

- maybe some group theory or maybe Partial differential equations would help.

The physics

- mechanics in one and several variables

- WAVE PHYSICS (So important for the schrodinger equation that it's ridiculous).

- Thermodynamics

When you have a great deal of numerical rigour and a lot of understanding of classical physics and the maths needed to understand what you really do, after this you should be able to ace a QM-course.

 

[zoner7]

ehh... at 15 you're school has taught you everything through precalculus? wow. That's impressive. I'm taking a guess that it isn't an american school

 

[JasonJo]

My best advice to a young math student is:

1) First and foremost, learn the beginning material EXTREMELY WELL. A lot of college students have a nightmare with trig, precalc, and other basic math subjects.

2) Get a hold of a good problem solving book. Polya's How to Solve It, Problem Solving Through Problems by Larsen (although this contains a lot of real analysis). But the idea is, introduce yourself to mathematical problem solving; what kind of techniques are used, how to use them, etc. You might not master these, but that's OK, you will be ahead of the curve and will be very experienced by the time you become a math major in college.

3) Learn some linear algebra. Linear algebra really isn't too big of a jump for a high school student who has taken precalc. But Linear Algebra contains a lot of proofs and some important ideas that are present throughout mathematics. You might be well served by taking a linear algebra course in the summer at a local university. This will probably also be your introduction to proofs, or the first class where you see rigorous mathematics.

Anyway, best of luck!

 

[Lateralis]

I taught myself the fundamentals of quantum physics using "Understanding Quantum Physics: A User's Manual, Vol. 1" by Michael A. Morrison. It is a fairly thick book, BUT, it succeeds where so many other books fail - it teaches you the physics! Morrison is exceptionally good at relating quantum concepts back to the world we live in and points out that quantum physics, actually, isn't so strange. Moreover, the writing style is relaxed and engaging - I used to read chapters of the book on the bus on the way into campus, on the train... even in bed at night! - and the physics is introduced at a sufficiently relaxed pace that you don't feel overwhelmed. In short, if I ever lecture quantum mechanics - and that is a life goal of mine - then this is the book I shall recommend as an introductory book.

Now, to be able to read the book though, you need to know calculus and algebra at the very least. He has a section on operator mathematics, but some very basic understanding of what an "operator" is would be useful. It is also important to understand Fourier analysis to some degree for the first couple of chapters (although Fourier methods are quickly dropped in favour of other more elegant and powerful methods).

 

[jtbell]

Most students first learn some QM not in a separate QM course that uses a textbook like Morrison or Griffiths, but rather, as part of an "introductory modern physics" course that comes right after freshman-level "general physics." These courses don't go very deeply into the mathematical details, but they do introduce the basic concepts and properties of the QM wave function, and show how to solve Schrödinger's equation for simple examples like the "particle in a box." They also give an overview of the solution for the hydrogen atom, usually leaving out the messy details. (e.g. they show you the differential equation for the $\theta$ part of the SE and say something like, "the solutions of this equation are called Legendre polynomials, which look like this...")

The math prerequisites are usually no more than basic calculus: derivatives and integrals. Many books at this level introduce or review the concepts of partial derivatives, differential equations and complex variables at the level needed to handle their examples and exercises.

These also books cover a lot of the historical and experimental background to QM. Dedicated QM textbooks usually assume that the student has already seen this material, and don't go into it very deeply.

 

[ajassat]

I'm on it - after everything people have said here is my study plan:

1) Review of all precalculus material - basic algebra, quadratics equations, cubic equations, cubic & reciprocal graphs, proportionality, probability, functions of graphs, sine functions etc...

2)Binomial Theorem

3) Introductory Calculus for students who have finished precalculus. Using the book Crowell's Calculus. Also some partial differential equations

4) Introductory Linear Algebra

5) Complex analysis

6) Fourier analysis

 

[Fearless]

ajassat: Like Jason Jo said; master the basics first which is more concrete than abstract. Because math like complex analysis and Fourier analysis are very abstract and even a seasoned physicist-student can get a bit shaken by those mathematical subjects.

But I think that the more important thing here isn't exactly what you do at this point in time. But being persistent about physics and mathematics. Doing it rigourous when you have the time and trying to solidify the concepts you learned at every level.

Because remember, the important thing isn't mastering it now, you have all the time in the world. Have some fun with it. :)

 

[clope023]

Most students first learn some QM not in a separate QM course that uses a textbook like Morrison or Griffiths, but rather, as part of an "introductory modern physics" course that comes right after freshman-level "general physics." These courses don't go very deeply into the mathematical details, but they do introduce the basic concepts and properties of the QM wave function, and show how to solve Schrödinger's equation for simple examples like the "particle in a box." They also give an overview of the solution for the hydrogen atom, usually leaving out the messy details. (e.g. they show you the differential equation for the $\theta$ part of the SE and say something like, "the solutions of this equation are called Legendre polynomials, which look like this...")

The math prerequisites are usually no more than basic calculus: derivatives and integrals. Many books at this level introduce or review the concepts of partial derivatives, differential equations and complex variables at the level needed to handle their examples and exercises.

These also books cover a lot of the historical and experimental background to QM. Dedicated QM textbooks usually assume that the student has already seen this material, and don't go into it very deeply.

not to derail the thread, but just wondering, is the introduction in mondern physics necessary to attempt a QM class if one would have the math prep for it?

 

[jtbell]

I wouldn't say it's strictly necessary, but many (perhaps most) students benefit from cycling through the subject (any subject, not just QM) repeatedly, at higher levels of sophistication and concentration each time. It's a big subject and can be approached in various ways. I studied at least parts of QM formally three times: undergraduate intro modern physics, undergraduate QM, and graduate-school QM. And then again when I had to start teaching it.

And I still don't claim to know all of it! :uhh:

 

[ajassat]

ajassat: Like Jason Jo said; master the basics first which is more concrete than abstract. Because math like complex analysis and Fourier analysis are very abstract and even a seasoned physicist-student can get a bit shaken by those mathematical subjects.

But I think that the more important thing here isn't exactly what you do at this point in time. But being persistent about physics and mathematics. Doing it rigourous when you have the time and trying to solidify the concepts you learned at every level.

Because remember, the important thing isn't mastering it now, you have all the time in the world. Have some fun with it. :)

I understand what you mean here. I think just studying the physics and maths and finding things out is having 'fun'. I am still working on the basics and slowly introducing myself to more complex things like binomial theorem.

If I do have a period where I don't understand something I usually go back and re-read with lots of concentration. My handwriting keeps on getting smaller and smaller :)