# Where should I start on learning about Quantum Mechanics

As you can tell from my name, I've heard about quantum mechanics over and over again because of Feynman's lectures etc, but I really don't know much about it. Where should I start in learning about it? Do I need to learn Calculus first, because the highest I am at right now is geometry and have just started on algebra II for the school year? Help would be appreciated!

FXF

Do not fancy it before calculus II....Even though I‘m taking Calc III and diff eq concurrently with Intro to quantum physics I still struggle at quantum physics. (In contrast calc III and diff eq are VERY easy..)

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Well, Feynman Lectures volume 3 is an excellent starting point. Try reading the first half a dozen chapters of volume 3, and you'll have some feel for the mathematics of quantum mechanics, and what makes it so weird.

If you want a less formal introduction, try Feynman's popular book QED: the strange theory of light and matter.

Fredrik
Staff Emeritus
Gold Member
You need some calculus and some linear algebra before you can study a standard introductory textbook. The concepts from linear algebra that you need to understand are: vector spaces, inner products, linear independence, orthonormal bases, linear operators, matrix multiplication, the relationship between linear operators and matrices, the adjoint operation, eigenvectors and eigenvalues. From calculus: limits, partial derivatives, integrals (including integrals from -∞ to ∞), series. You also need to understand complex numbers, but I wouldn't consider that either calculus or linear algebra.

AlonsoMcLaren (or anyone who feels the same way): Why does everyone emphasize calculus and not linear algebra?

I second the recommendation for "QED: The strange theory of light and matter". It's a great non-mathematical presentation of how QM can explain the weird behavior of light. (I haven't read the Feynman lectures on physics, so I can't comment on them).

vanhees71
Gold Member
2019 Award
In physics you need linear algebra and calculus! I think the most difficult thing in starting to learn physics is that one has to deal with vector or even tensor calculus before one has studied these subjects in the math course.

One should not learn these topics with quantum theory, because the challenge to comprehend quantum theory shouldn't be the mathematics since the really weird thing about it is the physics. I recommend to learn vector calculus first by studying classical physics (fluid dynamics and classical electromagnetism). Most intuitive is to have hydrodynamics as a picture for the various operations (div, grad, curl and various types of integrals related with these differential operators, Stokes's, Gauss's, and Helmholtz's theorems, etc.).

A short, but the the most useful intuitive introduction into this can be found in Sommerfeld's Lectures on Theoretical Physics, Vol. II.

Also, one should not start to learn quantum theory with photons, which is even more difficult than non-relativistic quantum mechanics of massive particles. The Feynman Lectures are a good starting point, particularly because of Feynman's famous "no-nonsense approach" to the subject. However, as many textbooks, it's overemphasizing the wave-mechanics formulation. After some familiarity with this approach one should come soon to the more abstract formulation in terms of Dirac's bra-ket formalism! A good intro for that is J. J. Sakurai, Modern Quantum Mechanics.

'The Quantum World' by John Polkinghorn is an interesting introduciton to qm.

jtbell
Mentor
Why does everyone emphasize calculus and not linear algebra?
Many of the introductory treatments of QM that students see (in the USA at least) introduce the necessary linear algebra concepts as they go along.

I agree that many students benefit from having studied linear algebra beforehand, so that they don't have to learn two sets of concepts (QM and LA) at once. On the other hand, some students don't get much out of a separate linear algebra class that's too abstract. They do better when they learn it in the context of applications like QM.

Also, most students here don't start studying QM by diving into a full-bore QM textbook like Griffiths or Sakurai or Shankar or Park or whatever. They get their first exposure in a second-year "intro modern physics" course that includes a few weeks of basic QM: the wave function, Schrödinger's equation, the particle in a box, tunneling, and an outline of the hydrogen atom.

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