[Quantum_Mechanics] Not too old to start a carrier in this Wfield

[HakimPhilo]

HELLO everybody and thank you!
My name is Hakim, 27-years, I'm a Moroccan graduated in computer science (specified in programming) with my master and I'm actually doing great...
My fascination with physics and science is deep... But I never studied any kind of physics or maths in school, except that I had the internet and with many many lectures I begin to understand more and more in physics.
What I want is to learn: Quantum Relativity and Quantum Physics.

*But what do I need in maths to learn it from A to Z?
*I just finished some parts about Algebra, and I want - and I thank everyone who could help me so much ! - to have a plan with all lessons I need to have to be able to do the maths of QR and QP... And then all the lessons and books about Classical Mechanics first, then a little bit of thermodynamics and finally all of QR and QP!

This may look to you to be completely impossible but just give me the lessons :) ! It will be helpful more than you may think !

THANKS IN ADVANCE!

 

[Sentin3l]

If you want to learn about relativistic quantum mechanics, you have a long way to go. A (very) conservative list would be:

Calculus
Linear Algebra
ODE's and PDE's
Real and Complex Analysis
Calculus of Variations (and other advanced calculus topics like integral equations)
Topology (This is an umbrella topic here, there are several areas of math that are covered under topology that you'll need to know)

As for the physics...nearly everything. QFT and Relativistic QM are current and highly debated research fields, and incorporate nearly all aspects of physics.

If you wish to continue in a self-study plan, considering you're just finishing up algebra, you have several years and a large ticket in textbooks to even understand these things at an elementary level. At a research level, you would possibly face 10+ years with no outside support from other Ph.D.'s

QM doesn't take as much, but you still have a long way to go.

 

[HakimPhilo]

I understand most of Quantum Mechanics concepts and also the General Relativity one I just need maths...
So indeed, what books do you recommend me?

 

[Sentin3l]

Concepts are very different from the actual mathematical framework. Relativistic QM is almost entirely math, it's "concept content" is minimal compared to other theories due to the fact it is cutting edge research. So if you want to understand it, you need the math not only behind QFT, but behind all of physics.

If you want books, check out the science textbook discussion page, they have book reviews and links to where you can buy them.

 

[WannabeNewton]

Relativistic QM is almost entirely math, it's "concept content" is minimal compared to other theories...

 

[HakimPhilo]

I like to have a sort of programme.

 

[DimReg]

Well, you definitely need to learn Calculus first. Physics without calculus is not very interesting, and is more likely to be confusing than informative. After that, physicists actually do a decent job of introducing required math as they go along, so I wouldn't spend too much time with your head buried in math textbooks.

For example, Taylor's classical mechanics introduces basic differential equations. Griffiths quantum introduces basic linear algebra (though nothing with matrices), and Griffiths E+M introduces vector calculus. So if you supplement these three books with a math methods book (say Boas), you will for the most part "know" undergraduate physics, including the math they use. (I would actually recommend these 4 books as a substitute undergraduate degree).

After that, I would focus on particle physics books rather than QFT books. Griffths particle physics and Halzen and Martins Quarks and Leptons are good for that. Both of these books teach you QFT, but from the perspective of the physical ideas, rather than the formalism.

These books suggestions aren't found from a large body of experience though. They're just the books I used in undergrad, and they worked great for me. There could be better choices.

Also, the idea that QFT is sparse on concepts is ridiculous. Just renormalization alone is a very deep subject that can be viewed from many different angles. It takes a lot more math to follow the arguments, but it doesn't mean the ideas aren't there.

 

[HakimPhilo]

Is KhanAcademy adequate for my learning?

 

[DimReg]

Is KhanAcademy adequate for my learning?

For Calculus, probably. For everything else, you probably need a dedicated book.

 

[Sentin3l]

Also, the idea that QFT is sparse on concepts is ridiculous. Just renormalization alone is a very deep subject that can be viewed from many different angles. It takes a lot more math to follow the arguments, but it doesn't mean the ideas aren't there.

I wasn't saying there are no concepts at all, but compared to classical physics where an intuitive sense of how the world behaves can guide you through the vast majority, QFT is a very rigorous mathematical undertaking. Speaking as an undergrad who is starting QFT (I'm doing research with a high energy theory prof.) the difference is immense. While some parts are more physically realizable than others, learning QFT through the concepts alone is something I would not consider possible.

 

[WannabeNewton]

Sentin3l I would have to agree with you on that personally not only for QFT but also for things like GR. It's too bad though because the complex conceptual subtleties of classical mechanics are what made it fun IMO. I've only seen a handful of books on classical mechanics where the mathematics completely drowns out the physics. On the other hand I've seen that quite a bit for QFT and GR texts (grad texts in particular); it's like they forgot they were physics books and not math books- I'm sitting there wondering where the heck is the physics? I certainly agree with you that the difference is immense.

 

[HakimPhilo]

If you want to learn about relativistic quantum mechanics, you have a long way to go. A (very) conservative list would be:

Calculus
Linear Algebra
ODE's and PDE's
Real and Complex Analysis
Calculus of Variations (and other advanced calculus topics like integral equations)
Topology (This is an umbrella topic here, there are several areas of math that are covered under topology that you'll need to know)

As for the physics...nearly everything. QFT and Relativistic QM are current and highly debated research fields, and incorporate nearly all aspects of physics.

If you wish to continue in a self-study plan, considering you're just finishing up algebra, you have several years and a large ticket in textbooks to even understand these things at an elementary level. At a research level, you would possibly face 10+ years with no outside support from other Ph.D.'s

QM doesn't take as much, but you still have a long way to go.

So I need first Linear Algebra:
Vectors and spaces
Matrix transformations
Alternate coordinate systems (bases)

Then: Trigonometry and Pre-Calculus
Graphing lines
Functions and their graphs
Polynomial and rational functions
Exponential and logarithmic functions
Basic Trigonometry
Trig identities and examples
Parametric equations and polar coordinates
Conic sections
Systems of equations and inequalities
Sequences and induction
Probability and combinatorics
Imaginary and complex numbers
Hyperbolic trig functions
Limits

Then: Calculus
Limits
Taking derivatives
Derivative applications
Indefinite and definite integrals
Solid of revolution
Sequences, series and function approximation
AP Calculus practice questions
Double and triple integrals
Partial derivatives, gradient, divergence, curl
Line integrals and Green's theorem
Surface integrals and Stokes' theorem
Divergence theorem

Then: ODE's and PDE's
%A little bit scared ^^
But any courses?

Then: Real and Complex Analysis
But any courses?

Then: Calculus of Variations
But any courses?

THANK YOU!

 

[Sentin3l]

So I need first Linear Algebra:
Vectors and spaces
Matrix transformations
Alternate coordinate systems (bases)

Then: Trigonometry and Pre-Calculus
Graphing lines
Functions and their graphs
Polynomial and rational functions
Exponential and logarithmic functions
Basic Trigonometry
Trig identities and examples
Parametric equations and polar coordinates
Conic sections
Systems of equations and inequalities
Sequences and induction
Probability and combinatorics
Imaginary and complex numbers
Hyperbolic trig functions
Limits

Then: Calculus
Limits
Taking derivatives
Derivative applications
Indefinite and definite integrals
Solid of revolution
Sequences, series and function approximation
AP Calculus practice questions
Double and triple integrals
Partial derivatives, gradient, divergence, curl
Line integrals and Green's theorem
Surface integrals and Stokes' theorem
Divergence theorem

Then: ODE's and PDE's
%A little bit scared ^^
But any courses?

Then: Real and Complex Analysis
But any courses?

Then: Calculus of Variations
But any courses?

THANK YOU!

I assume you're referring to khanacademy?

KA is great for review or high school. Khan unfortunately (to my knowledge) did not go much farther than linear algebra or ODE's in his math education, so he has no courses on the more complex material. To really learn the stuff you need a more rigorous introduction. Go ahead and get the algebra (NOT linear algebra) and basic calculus from KA, then once you're done with that get "Mathematical Methods in the Physical Sciences" by Mary Boas. You should try or work through every problem in the book.

Once you're done with that you need to then get textbooks and learn on your own. Unless you have access to a course at your local university, you will have to teach yourself as I have never seen any online free courses of any of the advanced maths (although you may be able to find lecture notes).

An easy guide to follow is the one given on the string theory website, found http://superstringtheory.com/math/math1.html(note that there are three pages). I'm not sure how the math for string theory and the math for QFT stack up, but I imagine they would be fairly similar.

This is not even touching the physics you will have to know to understand QFT, which is of itself, a very large undertaking. I'm not going to lie to you, learning this stuff on your own is going to be very hard.

 

[HakimPhilo]

http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html#mechcon

Is this a nice tool?

 

[jtbell]

Hyperphysics is a good supplement to a textbook, or for review. For actually learning the material, you need a textbook that has decent exercises, IMO. The exercises are crucial. If I had a dollar for every student who told me, "I understand the material when I read it, I just can't do the exercises", I could have retired years ago.