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IndustriaL
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Hey, what kind of mathematics are needed to understand the bulk of QM and GR?
IndustriaL said:Hey, what kind of mathematics are needed to understand the bulk of QM and GR?
Kruger said:If you start with the Schrödinger equation you will see what you all need. i think if one can solve this equation he has understood the mathematical concept.
Do you actually mean Linear Differential Equations when you wrote "ODE"? ODE refers to ordinary differential equations to distinguish it from partial differential equations. ODE refers to non-linear diff eq.s. This was actually a class I took and I too was initially confused by the difference until I saw the text and spoke to the prof.dextercioby said:Not to go deep into details and the formalism and just gather a superficial knowledge of QM:linear algebra,calculus,complex analysis+special functions and ODE+PDE-s.
You have a long way to go, and a lot of classical physics to learn before you can start to appreciate or even understand QM or GR. Thinking about QM without the fundamentals (of classical mechanics -lagrangian and hamiltonian formulations, statistical mechanics and electrodynamics) laid down, is not the best way to go.IndustriaL said:Well, I'm a high school student and I'm very interested in Quantum Mechanics and General Relativity. I even took a class on classical physics here at school, but just the basic stuff.. I have pre-calculus down and just wanted to know what was needed to contribute thanks a lot :D btw.. that was a really quick response
Let's not exagerate now. There are many good books with zero math in them which doa good job at describing QM to the layman.Gokul43201 said:You have a long way to go, and a lot of classical physics to learn before you can start to appreciate or even understand QM or GR. Thinking about QM without the fundamentals (of classical mechanics -lagrangian and hamiltonian formulations, statistical mechanics and electrodynamics) laid down, is not the best way to go.
Topology is not required to learn QM.dextercioby said:There's only one way to learn the formalism of QM and that is:realizing this is theoretical physics and mathematics should be central.
Start with topology,the key ingredient of functional analysis.
Daniel.
dextercioby said:I don't reccomend a specific book on topology.You'll have to figure out by yourself what kind of mathematics you need to brush on,if you read the first 4 chapters of Bogolubov,Logunov & Todorov "Introduction to Axiomatic Quantum Field Theory",Benjamin/Cummings,1975.
Daniel.
dextercioby said:I don't deny you the right to disagree.After all,everyone is free to do whatever he likes,just as long as they don't make false claims,like "I know Quantum Mechanics"...
HackaB said:Okay, I'll take a look at that if they have it at the library. I've seen several books on QM authored by Bogolubov, so hopefully that was one of them.
HackaB said:Would you say that you know quantum mechanics?
Basement level?? Clarify please.aav said:For basement level QM math, I'd recommend something like Cohen-Tannoudji, especially Ch 2 (plus complements) for the mathematical foundations.
Why do you consider using as much math as possible "the right way.?dextercioby said:Him & Landau are Russia's greatest theorists.
Nope.It's not modesty,but I'm learning QM the right way.Using as much mathematics as possible.
Daniel.
pmb_phy said:Basement level?? Clarify please.
I took quantum mechanics in both undergrad and graduate school. I no class and in no text did I ever read anything which referred to topology. E.g. see
http://www.geocities.com/physics_world/qm/state_space.htm
What is the benefit of using topology in QM?
Pete
And yet I know functional analysis and never studied topology. What you're saying is similar to saying that real analysis is a prereq for calculus. While true, one never needs to study real analysis to understand most if not all of calculus. I took real analysis because my second major was math and was required but it was a very difficult course and only served to give me more confidence in calculus.aav said:Topology as a mathematical prerequisite for functional analysis, when you start discussing stuff like Lebesque integration, measure theory, L2 spaces, the Riesz-Fischer theorem, generalized functions, etc etc which are required in a rigorous formulation of the math of QM.
pmb_phy said:What you're saying is similar to saying that real analysis is a prereq for calculus. While true, one never needs to study real analysis to understand most if not all of calculus.
Pete
True. Far too short. I was once so naive as to think I could learn all branches of math that has ever been applied to anykind of physics. One problem with that. By the time you learn the last you have forgotten a lot of the first.aav said:Yes, I agree, from a practical point of view real analysis is not needed for calculus, but the suggestion Daniel gave (as I understand it) was to study QM from a axiomatic point of view. I simply recommended doing the "usual" math first...
But alas, Art is long and life is short...
X-43D said:I think it doesn't much more than multivaraite calculus, linear algebra and differential geometry/topology to understand GR and QM.
Please give an example where group theory is absolutely necessary. Thanks.selfAdjoint said:Well if you want to go beyond the obvious with spin, you need a little bit about groups and representations