What Math Do I Need to Know for Quantum Mechanics?

[JasonRox]

I searched and all I could find is recommended texts.

I was just wondering was areas of mathematics should I know before cracking open a book on QM.

I know they give you pre-requisites and that can give some hints, but sometimes that isn't enough. I'm sure some students experience the I-wish-I-took-calculus-before-PHYS101.

In other words, what should I know, and what do you wish you knew before going into QM.

Thanks.

 

[Fredrik]

You need to know some calculus (derivatives, integrals, etc) and linear algebra, and you have to understand complex numbers.

When you understand everything that I wrote here, you're off to a good start. If you also learn a little about derivatives, integrals and complex numbers, you will be well prepared.

 

[Chronos]

The ability to solve first order derivatives will be a huge advantage [hint: not all of them have solutions you can relate to reality].

 

[danitaber]

In other words, what should I know, and what do you wish you knew before going into QM.

Thanks.

In the Beginning. . . I wished I knew all about Fourier Transforms, all of the basics from linear Algebra (inner product, bases, orthonormality, etc.), familiarity with the more common second-order differential equations, everything about Hilbert spaces and vector spaces (also found in linear algebra) bra-ket notation (very helpful wikipedia entry).

And I'm only on Chapter 1.

What I really wish I knew is where to find a QM text that doesn't assume one knows everything already

Good Luck, happy fishing!

 

[JasonRox]

danitaber, that's exactly I was looking for. I heard eigen values and vectors are part of it as well.

Um... sounds like I can start in a few months.

 

[ZapperZ]

I searched and all I could find is recommended texts.

I was just wondering was areas of mathematics should I know before cracking open a book on QM.

I know they give you pre-requisites and that can give some hints, but sometimes that isn't enough. I'm sure some students experience the I-wish-I-took-calculus-before-PHYS101.

In other words, what should I know, and what do you wish you knew before going into QM.

Thanks.

I'm going to be rather crude and shamelessly plug my Journal by suggesting that you read Part 3 of my "So You Want To Be A Physicist" essay. It's hard to pick a few parts of math and say you should know those to be able to do QM. It is much more prudent to arm yourself with as wide of a mathematical expertise as possible. The book that I recommend in that essay is something I have absolute confidence in, and I will be highly surprised if you don't find it useful, not just for QM, but for your other physics classes.

Zz.

 

[danitaber]

Speaking of ZapperZ's Journal:
I always enjoy reading it. I will look for this book, even if I have to set aside cash for several months to actually buy it. I'm trusting your judgement with my limited funds, ZapperZ.

And, yes, eigenvectors, -values, and -spaces are in QM, too. Like, in the first paragraph. . .

 

[RedX]

Well, I think you should learn calculus first. Then a little linear algebra (with only real numbers).

But I don't think you should really go crazy and learn real analysis so you'll better understand calculus or go into linear algebra with complex numbers.

Instead, after calculus and real linear algebra, I recommend:

Shankar's Principles of Quantum Mechanics , 1st chapter (75 pages on the math you'll need to understand the rest of the book). I mean you could read what the mathematians are writing but you know mathematicians are kind of (on crack). Someone with experience in QM might be able to better emphasize the mathematics that are needed for QM. For example, if you check out a mathematics book on Hilbert spaces, then since the mathematical definition of a Hilbert space is a inner product space whose elements are all normalizable to unity, you won't be able to work with continuous eigenstates in physics (like position or momentum eigenstates), because those are only normalizable to the delta(0). Shankar talks about both.

 

[ZapperZ]

Speaking of ZapperZ's Journal:
I always enjoy reading it. I will look for this book, even if I have to set aside cash for several months to actually buy it. I'm trusting your judgement with my limited funds, ZapperZ.

And, yes, eigenvectors, -values, and -spaces are in QM, too. Like, in the first paragraph. . .

Thank you.

Just to convince you a bit more, the book contains a chapter on unitary transformation that is frequently used in QM. For example, given a 2x2 matrix, how do you go about finding the eigenvalues of that matrix? After you found it, how do you find the eigenvectors? And then how do you unitarily transform it to that particular eigenstate.

Beyond that, this is one of the few books that has a complete chapter on calculus of variation. If you have done this, you would never be puzzled on where and how the Lagrangian/Hamiltonian formulation of classical mechanics came from.

You won't be sorry.

Zz.