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Hey, what kind of mathematics are needed to understand the bulk of QM and GR?

- Thread starter IndustriaL
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Hey, what kind of mathematics are needed to understand the bulk of QM and GR?

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For GR,well,calculus and linear algebra is more that enough to understand the nongeometrical exposure by Dirac [1].

Daniel.

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[1] P.A.M.Dirac "General Relativity",1975.

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chroot

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John Baez has a nice link about "how to learn math and physics". As far as QM is concerned, you will need at least:IndustriaL said:Hey, what kind of mathematics are needed to understand the bulk of QM and GR?

Calculus

Multivariable calculus

Linear algebra

Ordinary differential equations

Partial differential equations

Complex analysis

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Complex analysis is not necessary to use/understand QM.

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Daniel.

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Tom Mattson

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The trouble with this is that the Schrodinger equation and the deductions that follow from it do not exhaust the whole of QM. For instance, how can you derive spin from Schrodinger? You can't.Kruger said:

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Quantum mechanics doesn't put much emphasis on differential geometry (Spivak style) but instead makes heavy use of algebra.

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Daniel.

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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.

Pete

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Gokul43201

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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:

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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.

Pete

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Gokul43201

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But the OP was suggesting that he wanted to learn QM the mathematical way.

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Start with topology,the key ingredient of functional analysis.

Daniel.

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What topology book do you recommend?

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Daniel.

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Topology is not required to learn QM.dextercioby said:

Start with topology,the key ingredient of functional analysis.

Daniel.

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Daniel.

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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.dextercioby said:

Daniel.

Would you say that you know quantum mechanics?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"...

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For someone just starting out, IMHO starting out with topology to learn the mathematics of QM would probably be... overwhelming. It is certainly possible to approach the subject at different levels of mathematical rigor and sophistication, but why start at the penthouse?

For basement level QM math, I'd recommend something like Cohen-Tannoudji, especially Ch 2 (plus complements) for the mathematical foundations. Then Dennery and Krzywicki (notice they start out with complex analysis). That's a whole lot of math right there, enough to keep you busy for quite a while.

Then afterwards, after you get a "feel" for the math, you can revisit it again from a more rigorous perspective starting with, say, Kelley's

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Him & Landau are Russia's greatest theorists.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.

Nope.It's not modesty,but i'mHackaB said:Would you say that you know quantum mechanics?

Daniel.

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