# Prerequisites of Quantum Mechanics

by asen7
Tags: mechanics, prerequisites, quantum
 P: 13 Hi everyone, I am a college freshman, and was interested in this topic. So I was wondering, where does one draw the distinction between the physics and chemistry of quantum mechanics? Or in other words, what topics do quantum chemistry encompass, and what does quantum mechanics/physics encompass? I was also wondering, what are the science class and math class prerequisites for quantum mechanics? And I am a bit new to college, so could you list the order of math one takes to cover all the math prerequisites (from the introductory classes to the more advanced classes)? And the order of the science classes to cover the science prerequisites? Thank you
 P: 2 Quantum chemistry mathematically describes the fundamental behavior of matter at the *molecular* scale Quantum physics is a branch of physics providing a mathematical description of the dual particle-like and wave-like behavior and interaction of matter and energy at the *atomic or subatomic* scale as for the classes required, I cannot help you there: Im not in college yet
 P: 13 Thanks, Anyone know the classes/prerequisites though?
 P: 883 Prerequisites of Quantum Mechanics On the physics side, you should first take your school's freshman physics sequence. On the math side, you need multivariable calculus. Differential equations would be very helpful but you can probably learn what you need as you go. Helpful but probably not strictly necessary are linear algebra and Fourier analysis.
 P: 13 is fourier analysis a seperate math course?
 P: 25 On the physics, you'll need to have foundation knowledge of how a wave/particle behaves or should behave, wave equations of different wave functions. Fourier series may/may not be a different math course depending on your school curriculum.
 P: 31 Your college's registrar should tell you which classes are prerequisites for quantum mechanics classes. If you want to know what subjects you have to understand in order to follow quantum mechanics, here's a decent list: 1. Be comfortable manipulating complex numbers. 2. Understand linear algebra. Understand what it means to say "orthogonal matrices represent rotations" and "symmetric matrices represent inner products." Know what eigenvalues are. When you mix complex numbers and linear algebra, you get "unitary matrices represent rotations" and "hermitian matrices represent inner products." 3. Understand more linear algebra. What's a basis? An orthonormal basis? A change of basis? What does it *mean* when we say that a unitary matrix changes one orthonormal basis into another? 4. Eventually, understand even more linear algebra---what's the matrix exponential? What's the spectral theorem? What do they *mean*? When I was first trying to figure out how quantum mechanics worked, I read about how Schrodinger's equation was solved for the hydrogen atom and figured that differential equations were really important. It turns out that they aren't; the harmonic oscillator, the particle in a box, and the hydrogen atom are really the only three differential equations that anybody ever seems interested in solving, and the solutions are generally handed to you from the start. Once the solutions are handed to you, then you apply a bunch of linear algebra techniques to combine and interpret them. So linear algebra is where most of the real insight lies.
P: 13
 Quote by Penn.6-5000 When I was first trying to figure out how quantum mechanics worked, I read about how Schrodinger's equation was solved for the hydrogen atom and figured that differential equations were really important. It turns out that they aren't; the harmonic oscillator, the particle in a box, and the hydrogen atom are really the only three differential equations that anybody ever seems interested in solving, and the solutions are generally handed to you from the start. Once the solutions are handed to you, then you apply a bunch of linear algebra techniques to combine and interpret them. So linear algebra is where most of the real insight lies.

So will I need much multivariable calculus? or vectors?

And the hamiltonian operators and eigenvalues, and other operators can be found in which level of math textbook? Or will it be found in a quantum mechanics textbook?
P: 271
 Quote by Penn.6-5000 Your college's registrar should tell you which classes are prerequisites for quantum mechanics classes. If you want to know what subjects you have to understand in order to follow quantum mechanics, here's a decent list: 1. Be comfortable manipulating complex numbers. 2. Understand linear algebra. Understand what it means to say "orthogonal matrices represent rotations" and "symmetric matrices represent inner products." Know what eigenvalues are. When you mix complex numbers and linear algebra, you get "unitary matrices represent rotations" and "hermitian matrices represent inner products." 3. Understand more linear algebra. What's a basis? An orthonormal basis? A change of basis? What does it *mean* when we say that a unitary matrix changes one orthonormal basis into another? 4. Eventually, understand even more linear algebra---what's the matrix exponential? What's the spectral theorem? What do they *mean*? When I was first trying to figure out how quantum mechanics worked, I read about how Schrodinger's equation was solved for the hydrogen atom and figured that differential equations were really important. It turns out that they aren't; the harmonic oscillator, the particle in a box, and the hydrogen atom are really the only three differential equations that anybody ever seems interested in solving, and the solutions are generally handed to you from the start. Once the solutions are handed to you, then you apply a bunch of linear algebra techniques to combine and interpret them. So linear algebra is where most of the real insight lies.
This. The language of quantum mechanics is really linear algebra!
P: 6,863
 Quote by romsofia This. The language of quantum mechanics is really linear algebra!
It's also multi-variable calculus!!!

One cool thing about QM is that you find out that multi-variable calculus and linear algebra can be two different ways of looking at the same thing.
P: 6,863
 Quote by asen7 So will I need much multivariable calculus? or vectors?
Not really. You'll need to be comfortable talking in that language. You won't need to do proofs.

 And the hamiltonian operators and eigenvalues, and other operators can be found in which level of math textbook? Or will it be found in a quantum mechanics textbook?
Depends on the specific class.
 P: 13 This is more of a self-study for me. So can anyone recommend any good (as in very specific, detailed, clear, and understandable instruction) quantum mechanics textbooks preferably from introductory quantum mechanics textbooks to a few "classes" a bit more advanced than that? Thanks everyone, I really do appreciate the responses so far.
 P: 492 Griffith's is normally a really good place to start. I read the Feynman lectures for a different perspective on things, and they're meant to be somewhat introductory as well.
 P: 31 Volume three of the Feynman Lectures does an excellent job of explaining the intuitive underpinnings of quantum mechanics---what superpositions are, what the hamiltonian does, what changes of basis are, and so on. The downside is that Feynman takes his time in getting to how his explanations relate to the explanations you'll see in other books. For example, he introduces the concept of "stationary states" (which everyone else calls "eigenstates") in section 7-1. He first uses stationary states indirectly to solve a problem in section 8-6. In section 9-1 he explicitly computes the stationary states of the ammonia molecule. But it isn't until section 11-6 that he finally says, "Physicists usually call the states |n> 'the eigenstates of H.' " So he's strung you along for four chapters explaining what eigenvectors are and how to use them, but unless you're particularly clever you don't realize that you're using eigenvectors until section 11-6. So it can take awhile to relate Feynman's explanations to all the other textbooks, even though they eventually link up. The upside to Feynman is the same thing---that he spends four chapters explaining how eigenvectors work before dropping the E-word. A lot of other books just assume that you're familiar enough with linear algebra to know what eigenvectors are, so they'll just use eigenvector methods without telling you why. Feynman assumes nothing---he teaches you how to multiply two matrices in section 11-1. So in my opinion Feynman is by far the best place to get your linear algebra intuition. I wish I could recommend a good linear algebra book but I'm not particularly enthusiastic about any of them. I first learned linear algebra from "Schaum's Outline of Linear Algebra." It's cheap, it's thorough, and it shows its work in calculations. But it's also *too* thorough (it covers a lot of stuff you won't need) and more abstract than intuitive. Schaum's is a lot better than nothing, but it might not be the best for you.
 P: 13 When I was going over the topic, I found something about QED and QCD which seem interesting. But how is QCD and QED different from quantum mechanics, and what can you do with QED and QCD? If I wanted to focus in more on these two branches, would I need to learn any more levels math other than the ones listed above? Thank you very much, I really appreciate the responses so far.

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