
#1
Jan814, 11:27 PM

P: 31

I have been aiming to venture further into my understanding of quantum mechanics( Past classical mechanics).I see many thread
s here but few with complex mathematical formuli. Is it that nobody bothers to list them or have I not looked close enough? To get a deep understanding of the universe, how far into calculus must one go? Is it just being able to solve differentiable equations? 



#2
Jan914, 12:05 AM

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There's no "just" about being able to solve differential equations :) You also need matrix algebra.
The actual math in QM is not all that esoteric as far as math goes. 



#3
Jan914, 12:15 AM

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Algebra
Trigonometry Calculus (single and multivariable) Linear Algebra Differential Equations I have heard Vector Calculus helps too... though i haven't taken that personally. 



#4
Jan914, 01:00 AM

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What math is required for physics?
Conceptual Physics: very little math: addition, subtraction, multiplication, division, squaring and squarerooting numbers. (IMHO, Conceptual Physics is the most important. If you have a conceptual understanding of what's going on, you can go deep later in your education. If you're a formulapusher, you won't go too far in Physics.)
Physics: Algebra (although many of the formulas you use are either derived or proven using calculus) High School AP Physics B: Algebra (plus a good understanding of Conceptual Physics) High School AP Physics C, Mechanics and E&M: Algebra and some Calculus (derivatives and antiderivatives and integrals of polynomials and simple trig functions. Chain rule and Usubstitution and rarely integrals involving 1/x, differential equations [separation of variables only, i.e. F=ma becomes F=m (dv/dt)]). If you don't know ANY calculus, you can still get a 4/5 on the AP C exams provided you ACE algebra stuff. College Physics if you're NOT a Physics or Engineering major: Pretty much the same as High School regular Physics. College Physics if you're ARE a Physics or Engineering major: Not too much difference from AP C High School Physics! It's a little tougher, and you'll be competing against a higher caliber of students. You'll also see some thermo and fluids thrown in. College Physics if you ARE going for a Masters: Know your math. Know ALL your math. But make sure you're VERY good with Conceptual Physics. Otherwise all the math in the world will do you no good at this level. College Physics including Quantum: "differential equations" ARE part of Calculus. If you're a Physics major, or Engineering major, or an Astronomy major (assuming your university offers it as a separate major) To get a "deeper understanding of the universe" at ANY level, you simply need to learn more math. To understand the universe as no one before you ever has understood it, you need to make up your own math like Newton did! (he coinvented Calculus to prove Earth can be simplified as a point mass). 



#5
Jan914, 01:19 AM

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I've not been terribly impressed with courses called "conceptual physics" as a foundation for more advanced study. But that may not be what you mean. Physicists do seem to think of math differently to mathematicians though  they tend to be less formal or rigorous, treating it like a language. I think that's the central point: got used to using math concepts to describe things in nature. It's why we set lots of wordy problems and use lots of pictures. 



#6
Jan914, 03:45 PM

P: 448

Because math has nothing to do with nature. Physics, being a natural science and all, does however.
In physics we use math to uniformly and as precisely as possible describe a physical situation , knowing math is meaningless without understanding the natural aspect of physics. Edit: I guess the post I was replying to was deleted. Oh well. 



#7
Jan914, 03:45 PM

P: 31

Dunno  I agree that pushing formulas won't get anyone far but that's the same with math in general.
I can't seem to understand this statement. Can you explain with proof/valid reasoning. If I were to learn calculus/linear algebra and conceptual physics, what would be left to fill in my understanding of quantum physics? Just memorizing 100 formulas? 



#8
Jan914, 06:15 PM

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By "pushing formulas" I am talking about the approach where you memorize the "correct equation" or formula to use for each situation ... you put the numbers in the equation and get the right answers out.
Think of math as a language and "pushing formulas" as the "tourist phrasebook" version of that language. 



#9
Jan914, 06:45 PM

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I taught Integrated Physical Science at a different high school. I actually liked it better than Conceptual Physics for the freshmen. It was a little bit of Physics, a little bit of Astronomy, and a little bit of Earth Science thrown together. But I was told that Integrated Physical Science doesn't transfer to the UC colleges, while Conceptual Physics does. It's too bad. Unless I deviate a little from the syllabus (which I always do!), students will go through our high school not knowing why summer is warmer than winter, and not knowing why the moon goes through phases. 



#10
Jan914, 08:38 PM

P: 31

Simon Bridge, are you trying to say: unless you want to conduct expirements and calculate how much one H atom heats up when hit by a gamma ray, formulas prove no use?




#11
Jan1014, 12:37 AM

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I'm saying you won't get far just by memorizing algorithms. You need to develop an understanding of the principles that underlie the formulas and equations. I take it you are not saying that if you have the formulas you don't need to understand them? For instance  how does it make sense to talk about a single H atom "heating up" as a result of the interaction with a gamma ray? The answer may just be a matter of finding the right formula  but science education is supposed to train you to solve problems where there is no known correct formula or the correct one is in dispute. I think you'll see it more clearly if you follow the introductory physics threads in PF. Meantime have a look at: Eric Mazur: Understanding or memorization: Are we teaching the right thing? Also the How to study physics guide from Texas U. 



#12
Jan1014, 12:49 AM

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You tend to get do better in physic when you have strong background in trigonometry,calculus and algebra ESPECIALLY linear algebra :)




#13
Jan1014, 07:38 AM

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To answer your question, the minimum amount of math required to do physics is whatever is in Mary Boas's "Mathematical Methods in the Physical Sciences" text. That is as clear as an unambiguous of an answer that I can give. Whether you believe it or not, that's your problem. Zz. 



#14
Jan1014, 12:21 PM

P: 209

Group Theory, Differential Geometry, Hilbert Space, and Topology are also important to modern physics. No one ever seems to mention those. You pretty much have to be a mathematician to get into theoretical physics.




#15
Jan1014, 10:34 PM

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#16
Jan1214, 07:38 AM

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For example  http://www.physicsforums.com/showthread.php?t=731782 And one can look through the Advanced Physics homework forum for problems in QM/QP. This site has a good overview of the math topics one would need to master with respect to physics. http://superstringtheory.com/math/math1.html Gerard t'Hooft has a good webpage that discusses physics and math. http://www.staff.science.uu.nl/~hooft101/theorist.html Here are a couple of examples from universities (in the UK) that discuss math in conjunction with physics. http://www.bristol.ac.uk/prospectus/...missions_joint http://www3.eng.cam.ac.uk/admissions...hs_advice.html Of course, one could read various physics texts and review examples of the mathematics involved in describing the physics of various phenomena. In QM/QP, would need some proficiency in partial differential equations, vector analysis/linear algebra, complex analysis, and probably statistics. 


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