/sci/ - Science & Math » Thread #10936319

300KiB, 1600x1073, QMJobCrop.jpg

View Same Google iqdb SauceNAO

Self-study:Road to Quantum Mechanics

Anonymous Mon 02 Sep 00:40:55 2019 No.10936319 View Reply Original Report

Quoted By: >>10936615 >>10937447 >>10938027

Hi there!
I am interested in learning Quantum Mechanics. The problem is that my math ans physics background are kind of poor. At the moment I am studying Philosophy but I am getting tired of fancy talk without any math and science. Last time I seriously studied them was 6 years ago. I used to have some basic Physics and Chemistry secondary school knowldge. Mathwise, my knowledge is up to Calculus and Linear Algebra(I was never good at LA). Any tips,advice, resource and/or material recommendations are welcome.

Anonymous

View Same Google iqdb SauceNAO 660AE7E5-EC76-4EDA-9531-D155EB0B (...).png, 451KiB, 822x904

Anonymous Mon 02 Sep 2019 00:44:14 No.10936323 Report

Quoted By: >>10936366 >>10938027 >>10940124

Get better at LA, do some basic applied complex analysis and diff eq, learn lagrangian mechanics, maybe read a chapter or two of dummit and foote or something

Anonymous

Anonymous Mon 02 Sep 2019 01:17:16 No.10936366 Report

Quoted By: >>10938703

>>10936323
Nice filename.

Anonymous

Anonymous Mon 02 Sep 2019 01:35:16 No.10936385 Report

Quoted By: >>10937191 >>10940124

If you know physics 101 and enough calculus so that you know what a gradient operator is, you can learn QM. Pick up Griffiths textbook. It is the standard undergraduate textbook, and to be honest there isn't much else in graduate quantum mechanics that isn't found in that book.

Any linear algebra you will learn along the way, there is no need to study it first.

As a sidenote, despite what philosophers believe, QM is not the cutting edge in physics. This is physics for the year 1930 (well there is some later stuff if you read about Bell's theorem, no-cloning, and all that). You will still not be qualified to philosophize about physics after learning this.

Anonymous

Anonymous Mon 02 Sep 2019 03:45:04 No.10936615 Report

Quoted By: >>10937191 >>10937452 >>10938027 >>10940124

>>10936319
Shankar's textbook is surprisingly self-contained despite the often lackluster prose. Also you'll figure out how much more math you need. Realistically you need to get better at LA, pick up a few things from diff eqs. (because as any undergraduate knows the best part of quantum is deriving the Hermite, Legendre and Laguerre polynomials) and, since you'll see contour integration show up a few times, some complex analysis.

Anonymous

Anonymous Mon 02 Sep 2019 11:40:44 No.10937191 Report

Quoted By: >>10938027 >>10939283

>>10936385
>>10936615
Hoe long do you think the whole endeavour will take?

Anonymous

Anonymous Mon 02 Sep 2019 12:46:40 No.10937321 Report

Quoted By: >>10937465 >>10938027 >>10939300 >>10940124 >>10940148

Here's the mathematical concepts you will need to learn for Quantum mechanics. I laid it out based on the book that I own, "Molecular Quantum Mechanics" by Peter Atkins and Ronald Friedman.

Complex numbers
Differential equations
Vectors (definitions, operations, graphical representations, vector differentiation)
Matrices (addition/multiplication, determinant, eigenvalue equations)
Scalar and vector functions (gradient, divergence, curl)
Fourier series and Fourier transforms

Linear operators
Eigenfunctions and eigenvalues
Commutation and non-commutation
Construction of operators
Integrals over operators
Dirac bracket and matrix notation
Hermitian operators

It also goes into relevant topics of Group Theory.

Anonymous

Anonymous Mon 02 Sep 2019 13:47:42 No.10937447 Report

Quoted By: >>10940124

>>10936319
Griffinths if you don't have a lot of mathematical background, Cohen if you do.
Linear Algebra is essential to quantum mechanics as mostly everything involves basis and representations/linear combinations.

It's a surprinsgly clear and powerful formalism once you got that nailed down.

Anonymous

Anonymous Mon 02 Sep 2019 13:50:08 No.10937452 Report

Quoted By:

>>10936615
For me, it was the applications and interplay to statistical physics.
The math of classical mechanics is more elegant than the one of QM tb h

Anonymous

Anonymous Mon 02 Sep 2019 13:54:37 No.10937465 Report

Quoted By: >>10940124

>>10937321
A good chunk of the theory of operators will be provided as a separate chapter or appendix in any good textbook.
You really just need to be rigorous in your calculations, to not be afraid of deriving big functions. An intuitive understanding of linear algebra and a mastery of the common proof techniques used really helps.

Anonymous

Anonymous Mon 02 Sep 2019 17:10:52 No.10937909 Report

Quoted By: >>10937943

What about probabilitiy? Is it needed? And if yes, to what degree?

Anonymous

Anonymous Mon 02 Sep 2019 17:29:41 No.10937943 Report

Quoted By:

>>10937909
The basics, really. StatMechs requires more probabilities

Anonymous

Anonymous Mon 02 Sep 2019 17:59:39 No.10938027 Report

Quoted By: >>10940124

>>10936319
>>10937191
This depends on the level you want to reach, if you want to be at the level of understanding the basics, having the first half of shankar down will take you far. >>10936323 >>10936615 >>10937321 mention some of the math you'll need at the beginning, but for some simple systems linear algebra more than suffices.
While Shankar is pretty good as an intro, books like Sakurai, Dirac, and Landau do a lot better at helping you develop mastery of the subject. Unironically David Tong has some nice notes as well, really on most undergrad/grad physics related to quantum. Also, there are some things not found in textbooks that are very helpful. Many of the papers of the people who worked in QM give a more intuitive feel for the subject, I'd recommend the Nobel lectures of Born, Bohr, Heisenberg, Dirac, and others. Many of their other papers are also gems, giving more justification as to why you might actually want to use those axioms in the first place, something many modern textbooks neglect. There's also more "modern" experimental developments that may interest you. On the theoretical side we have people like Gell-Mann and Hartle who developed the Consistent histories interpretation of quantum mechanics, essentially the copenhagen interpretation phrased in the language of path integrals (according to Gell-Mann) or Kochen and others who work on various no-go theorems in QM. On the experimental side there's some experiments that really test ones ability to grapple with quantum mechanics, usually the resolution is the understanding that special relativity and quantum mechanics are compatible. Things like this involve the delayed choice quantum eraser, the elitzur-valdman tester, and for completeness bell's inequalities, though I'd recommend watching sidney coleman's quantum mechanics in your face or reading the paper on the GHZ experiment instead, it really is pedagogically superior. Anton Zeilinger is basically the master of these kinds of experiments.

Anonymous

Anonymous Mon 02 Sep 2019 22:35:23 No.10938703 Report

Quoted By:

>>10936366
gotta shitpost on the go, ??

Anonymous

Anonymous Tue 03 Sep 2019 02:43:39 No.10939283 Report

Quoted By: >>10940124

>>10937191
A few months if you are reasonably bright and actually motivated enough to go through with it. Do some problems too.

You will likely have lots of gaps in your knowledge after you finish it, but at least you will have a better understanding of the formalism of ordinary QM, and can move onto something more advanced if you want

Anonymous

Anonymous Tue 03 Sep 2019 02:48:05 No.10939300 Report

Quoted By: >>10940124

>>10937321
Just going to add a few to your list.

- Probability theory: Expectation value, variance
- Euler's formula
- Energy and momentum
- Hamiltonian formalism

Good books: Griffiths, and Shankar

Anonymous

Anonymous Tue 03 Sep 2019 12:21:08 No.10940124 Report

Quoted By:

>>10936323
>>10936385
>>10936615
>>10937321
>>10937447
>>10937465
>>10938027
>>10939283
>>10939300
Thank you all for your answers guys!

Anonymous

Anonymous Tue 03 Sep 2019 12:29:37 No.10940148 Report

Quoted By: >>10940511

>>10937321
this is literally just retard complex analysis, abstract linear algebra+babby lin alg, multivariable calc and differential equations so basically nothing. also need probability I guess

Anonymous

Anonymous Tue 03 Sep 2019 16:20:57 No.10940511 Report

Quoted By:

>>10940148
>From great-post to shit-post
>Watch how this dullard anonymous turns a great informative piece of information into a fumbled mess of buzzwords and mindless condescension
>Click here for other ways to ruin a perfectly good post

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches