Quantum Mechanics Self-Study Guide: Books & Math Techniques

[Frankww]

I've planned my free time to study Quantum Mechanics. How do I begin? Which books should I use in my self-study? And how difficult will the mathematical tecnique be?
Thank you for all.

 

[malawi_glenn]

You should be good at calculus of one and several variables. Ordinary differential equations. Some partial differential equations. Linear algebra and statistics.

The best first school book in quantum mechanics is Griffiths "Introduction to quantum mechanics".
Also check out the tutorial section on this forum for free internet rescourses (like free science textbooks and so on, there is plenty for you there)

Also, you might start up with a textbook on "modern physics" to help you see WHY we discovered quantum mechanics and so on.

 

[olgranpappy]

I've planned my free time to study Quantum Mechanics. How do I begin? Which books should I use in my self-study?...

...you should buy the third volume of L. D. Landau's course in theoretical physics which is entitled "Quantum Mechanics."

That book will teach you quantum mechanics and it will also teach you how to kill Siberian polar bears with your bare hands.

The bear's pelt will keep you warm when the vodka runs out.

 

[jtbell]

How do I begin?

That depends on where you're starting from, of course. What courses in physics have you taken already?

Most students in the USA take a "real" QM course only after finishing (at least) a two-semester first-year college introductory calculus-based physics sequence which covers mechanics and electromagnetism, and a second-year introductory modern physics course which includes a brief introduction to the basic concepts of QM (the wave function and Schrödinger's Equation), and covers the key phenomena and experiments that led up to the development of QM.

Undergraduate QM textbooks generally assume that you have at least this much physics background.

 

[Daverz]

You'll need to understand at least Fourier decomposition and linear differential equations. Most basic QM books introduce separation of variables. You'll need only the most basic notions of probability and statistics (i.e. mean and standard deviation).

Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles
by Robert Eisberg and Robert Resnick has a good basic intro at about the sophomore university level in the U.S.

Shankar's Principles of Quantum Mechanics does a very good job introducing the math needed to move on to the next level, so I would suggest looking over the first couple of chapters of his book.

 

[olgranpappy]

You're probably lying. I don't think you know QM that well. Poser.

There is no need to be rude. We are simply trying to help someone who wants to learn quantum mechanics. Your posts have added nothing of interest to this thread--at least my first post was humorous (slightly?).

OP... In truth, Griffith's QM book is a very common starting point, but there are a lot of good books out there. (And some bad ones):

Sakurai "Modern Quantum Mechanics" is a good book that is used a lot. I've seen this used in graduate level classes as well, but it is fairly gentle.

Shankar "Principles of Quantum Mechanics" is a pretty nice big red book.

Cohen-Tannoudji's two volume set on QM has a lot of stuff in it.

Messiah's two volume set is my current favorite text on quantum mechanics, but maybe it is a little advanced and a little old-school (the same goes for Landau).

So, anyways, start with Griffiths or Sakurai, I would say.

 

[genneth]

The question is what you mean by quantum mechanics. There's the usual atomic physics based way, which is usually exposited along historical lines -- I can recommend Heisenberg's little book, Physical Principles of the Quantum Theory by Werner Heisenberg, which is cheap, though presumes a certain familiarity with calculus and linear algebra. For a meatier, more thorough book, one of the previously mentioned would be excellent. I'd get both -- it's not like the Heisenberg one is that expensive.

On the other hand, we're beginning to see that a better part of quantum mechanics isn't to do with the stuff of electrons, but really just a way to reason in the face of quantum uncertainty (or the tendency of the world to be disturbed by our measurements). There are various books that fall under quantum information theory. Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chuang is pretty good; it even covers the basics of linear algebra. Note that people who work in this field tend to use finite dimensional systems exclusively, and so usually by-pass a lot of the subtleties that occur in our usual descriptions of physics.

It depends on what you ultimately want to learn: quantum field theory or quantum computers?

 

[arunma]

I'll second Malawi's recommendation of David Griffiths' Introduction to Quantum Mechanics.

As for math, I'd say the minimum you need is two semesters of single-variable calculus, one semester of multi-variable calculus, a sophomore level course in ordinary differential equations, and a sophomore level course in linear algebra (the latter two are often taught as a single course). It's very important to remember the various techniques for doing integrals, such as integration by parts, trigonometric products, inverse trigonometric substitution, and partial fractions. It's also important to be fairly adept at linear algebra. So you don't need to know anything that advanced, you basically just need to have the math education that a science/engineering undergrad has after his second year.

Knowledge of partial differential equations would be useful, but it isn't necessary. Griffiths and other authors go through the PDE technique in the first couple of chapters. I got an A- in undergrad quantum without ever taking PDE.

Hope that helps!

 

[olgranpappy]

It depends on what you ultimately want to learn: quantum field theory or quantum computers?

The OP wants to learn quantum mechanics. That's what the man said. It is not at all clear why he should worry about any "ultimate" goal of quantum field theory or quantum computers...

perhaps you should explain yourself.

 

[deah]

hey...
what about from richard liboff?

 

[genneth]

The OP wants to learn quantum mechanics. That's what the man said. It is not at all clear why he should worry about any "ultimate" goal of quantum field theory or quantum computers...

perhaps you should explain yourself.

One involves calculus, the other doesn't. This can be a huge difference to someone striking out on his own.

 

[olgranpappy]

One involves calculus, the other doesn't...

Um... that doesn't make a lick of sense.

 

[genneth]

Um... that doesn't make a lick of sense.

The physics-y QM deals with particles, the states of which are wave functions -- vectors in an infinite dimensional Hilbert space. Things like momentum operators are derivatives (in the position basis), normalisation involves integration, etc. The information theory people deal with qubits, the states of which are vectors in finite dimensional spaces -- this simplifies a lot of the maths, whilst retaining the main concepts. Thus my question about what he really wants -- physics, to do with things like tunneling and field theory, or computing, to do with cryptography or teleportation.

 

[olgranpappy]

The physics-y QM deals with particles, the states of which are wave functions -- vectors in an infinite dimensional Hilbert space. Things like momentum operators are derivatives (in the position basis), normalisation involves integration, etc. The information theory people deal with qubits, the states of which are vectors in finite dimensional spaces -- this simplifies a lot of the maths, whilst retaining the main concepts. Thus my question about what he really wants -- physics, to do with things like tunneling and field theory, or computing, to do with cryptography or teleportation.

Yes, but why mention quantum computing explicitly? Just tell the OP to become an experimentalist... they don't know how to do calculus either.