# Tagged Questions

DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics ...

0answers
27 views

### Problem with Discrete Parseval's Theorem [migrated]

I think I must be missing something obvious, but I can't for the life of me see what it is. The discrete version of Parseval's theorem can be written like this: \$\sum_{n=0}^{N-1} |x[n]|^2 = ...
2answers
59 views

### Expanding two-variable function $f(x,y)$ over the complete sets $\{ g_{i}(x) \}$ and $\{ h_{j}(y) \}$

Quite often (see, for example, this PDF, 50 KB) when discussing the Born-Oppenheimer approximation the following assertion is made: any well-behaved function of two independent variables $f(x,y)$ can ...
2answers
105 views

### Why is $r'/r^2 = -1/r$? [closed]

If $r=r(t)$, why is $\frac{r'(t)}{(r(t))^2}$ = $\frac{1}{r(t)}$ where $'$ denotes the derivative? I saw it in a lecture. Can you please explain?
2answers
77 views

### Is there any phenomenon in physics which is sensitive to irrational numbers?

We can measure only rational numbers by our scale. Here is an example where irrational numbers does makes sense. If so then this question may have some theoretical importance. Is irrational numbers ...
1answer
113 views

### Does nature tetrate?

We see addition, multiplication and exponentiation in the natural formulae that make up physics. However, do we ever see tetration (repeated exponentiation) or higher hyper-operators in nature? ...
2answers
144 views

### Integer physics

Are there interesting (aspects of) problems in modern physics that can be expressed solely in terms of integer numbers? Bonus points for quantum mechanics.
1answer
77 views

### Spin(n) group SO(n) relation

Is it correct to state that the elements of Spin(n) fulfill a Clifford algebra and that the Lie group generators of Spin(n) is given by the commutator of the elements? If not, then what is the ...
2answers
113 views

### Suggestions on a particular arXiv publication on math needed for theoretical physicists [closed]

I'm going to start my PhD in a year and I'll be taking a gap year doing other stuff. But I also wanted to fill in the gaps in my math knowledge and I came across an arXiv publication called ...
2answers
59 views

### Equation describing magnetic hysteresis

So when you're looking at B-H curves for ferromagnetic substances, you often see these magnetic hysteresis curves, which occur, I gather, largely because of domain formation which has some reversible ...
1answer
139 views

### Universal Sequence and relationship of mathematics and reality [closed]

In "The Special and General Theory of Relativity" Einstein says: How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably ...
2answers
126 views

### Studying the logical structure of physics as a mathematical object per se? [closed]

I was wondering is there a branch of mathematical physics which studies the underlying logical structure of physics as a mathematical object per se? Let me explain what I mean by that. I'm ...
1answer
82 views

### Math for Thermodynamics Basics

I am studying Statistical Mechanics and Thermodynamics from a book that i am not sure who has written it, because of its cover is not present. There is a section that i can not understand: ...
1answer
181 views

### How deep can my knowledge of particle physics go without the maths?

Successfully just got my first question answered on here, and now time for the second. So I recently gained interest in particle physics and was wondering. By no means do I have the mathematical ...
1answer
71 views

### Taylor expansion of an integral in spherical co-ordinates

I've some difficulty deriving this equation from jackson electrodynamics (The equation after 1.30) \$\nabla^2 \Phi_a\left({\textbf{x}}\right)=-\frac{1}{\epsilon_0}\int_{0}^{R} ...
2answers
68 views

### continuity of the electric potential due to a surface charge

The Electric potential due to a charge distribution on a surface is : $\Phi \left ( x \right )=\int \frac{\sigma \left ( {x^{}}' \right )dx{}'}{\left \| x-x{}' \right \|}da$ I want to show that it's ...
3answers
215 views

### What is a dual / cotangent space?

Dual spaces are home to bras in quantum mechanics; cotangent spaces are home to linear maps in the tensor formalism of general relativity. After taking courses in these two subjects, I've still never ...
2answers
159 views

### How much pure math should a physics/microelectronics person know [duplicate]

I do condensed matter physics modeling in my phd and I was struck up learning quite an amount of physics. But while having done lot of physics courses, I see that if I learn pure math I would ...
0answers
107 views

### Is there a physical motivation to study finite fields?

Clearly finite groups are of immense value in physics and these are also substructures of fields. However I never came across any computations involving finite fields at university and so I never ...
1answer
104 views

### Topology for physicists [duplicate]

Which are the best introductory books for topology, algebraic geometry, manifolds etc, needed for string theory?
0answers
37 views

### How much math do I need to know to learn about quantum mechanics? [duplicate]

I am not good at math, so I needed to know if quantum mechanics involves a lot of math like, astrophysics for example, if it does, is there any book that can teach me this level of math?
11answers
749 views

### Is it possible for a physical object to have a irrational length?

Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational. If I were to use this ...
1answer
93 views

### Calculation of spherical Bessel functions - meaning of $\left(\frac{1}{x}\frac{d}{dx}\right)^{l}$

I'm trying to understand the calculation of spherical Bessel functions in chapter four of Griffiths' Introduction to Quantum Mechanics (2nd ed, p142). He gives ...
2answers
289 views

### Level of calculus required for physics [closed]

First time for me here so kindly let me know if I violate the rules - especially if this is a duplicate. After reading the page how to become a good theoretical phycist, I started a serious revision ...
0answers
192 views

### Interesting Math Topics Useful for Physics [closed]

What are some interesting, but less popular, math topics that are useful for physics that can be self-studied? Specifically, topics that might ultimately be useful in high energy theory (even if it is ...
1answer
157 views

### Impact of LHC on other science and technologies, in particular on mathematics?

The Large Hadron Collider (LHC) "remains one of the largest and most complex experimental facilities ever built" (Wikipedia); it may even be the most complex project in humankind's history (?). Such ...
2answers
385 views

### How should a theoretical physicist study maths? [duplicate]

Possible Duplicate: How should a physics student study mathematics? If some-one wants to do research in string theory for example, Would the Nakahara Topology, geometry and physics book and ...
2answers
262 views

### (Co)homology of the universe

In this post let $U$ be the universe considered as a manifold. From what I gather we don't really have any firm evidence whether the universe is closed or open. The evidence seems to point towards it ...
1answer
140 views

### Potential for charge distribution, finiteness

Consider a potential for charge distribution: $$v_H(\mathbf{r}) ~=~ \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}d\mathbf{r'}$$ where $\rho(\mathbf{r'})$ is the charge density. This ...
0answers
79 views

### Division algebras $(\mathbb{R,C,H,O})$ and discrete symmetry [closed]

I once saw a statement about the relation between division algebra(which means you can define a division in this algebra, there is a theorem saying we only have 4 kinds of division algebra, real R, ...
5answers
418 views

### Is physics rigorous in the mathematical sense?

I am a student studying Mathematics with no prior knowledge of Physics whatsoever except for very simple equations. I would like to ask, due to my experience with Mathematics: Is there a set of ...
3answers
338 views

### Does the axiom of choice appear to be “true” in the context of physics?

I have been wondering about the axiom of choice and how it relates to physics. In particular, I was wondering how many (if any) experimentally-verified physical theories require axiom of choice (or ...
1answer
137 views

### The use of Hall algebras in physics

I asked the same question in mo. I think maybe here there are more physics guys to help me. I once read a statement (not memorized precisely) that a certain physics quantity between two states of ...
1answer
274 views

### Reference for mathematics of string theory [closed]

I have a great interest in the area of string theory, but since I am more focused on mathematics, I was wondering if there is any book out there that covers mathematical aspects of string theory. I ...
1answer
218 views

### Mathematical definitions in string theory

Does anyone know of a book that has mathematical definitions of a string, a $p$-brane, a $D$-brane and other related topics. All the books I have looked at don't have a precise definition and this is ...
0answers
164 views

### Integrals given by Landau [closed]

Discussion about Landau's "Theoretical Minimum" has already been posted here. Unfortunately I couldn't find much about some examples of questions he gave to students. There are three questions in the ...
2answers
130 views

### Quantum Mechanics in terms of *-algebras

I'm currently trying to find my way into the geometric description of Quantum Mechanics. I therefor started reading: Geometry of state spaces. In: Entanglement and Decoherence (A. Buchleitner et ...
3answers
278 views

### Mathematics for Quantum Mechanics [duplicate]

What math should I study if I want to get a basic understanding of quantum mechanics and especially to be able to use the Schrodinger's equation.
4answers
545 views

### How do you do an integral involving the derivative of a delta function?

I got an integral in solving Schrodinger equation with delta function potential. It looks like $$\int \frac{y(x)}{x} \frac{\mathrm{d}\delta(x-x_0)}{\mathrm{d}x}$$ I'm trying to solve this by ...
1answer
180 views

### Why is physical space equivalent to $\mathbb{R}^3$?

Why is physical space equivalent to $\mathbb{R}^3$, as opposed to e.g. $\mathbb{Q}^3$? I am trying to understand what would be the logical reasons behind our assumption that our physical space is ...
5answers
306 views

### What is the meaning of following expresion $C=\frac{\delta Q}{dT}$ mathematicly

Our professor raised the following question during our lecture in Statistical Physics (even so it's related to Thermodynamics): Many text books (even wikipedia) writes wrong expressions (from ...
2answers
244 views

### Sum total distance of electrons on a spherical surface

What is the sum total distance between every possible pair of point charges when there are n point charges on a spherical surface? All point charges can only and are located on the infinitesimal ...
2answers
185 views

### Quantum mechanics on Cantor set?

Has quantum mechanics been studied on highly singular and/or discrete spaces? The particular space that I have in mind is (usual) Cantor set. What is the right way to formulate QM of a particle on a ...
0answers
54 views

### Is it possible to use the properties of quantum mechnics to develop a computer that develop mathmatical theory? [closed]

Is it possible to use the properties of quantum mechnics to develop a computer that develop mathmatical theory? I want some reference please, because i want to get into very detailed. Thanks in ...
7answers
691 views

### Why are radians more natural than any other angle unit?

I'm convinced that radians are, at the very least, the most convenient unit for angles in mathematics and physics. In addition to this I suspect that they are the most fundamentally natural unit for ...
2answers
58 views

### What is the minimal set of expectation values I need in a statistical model?

At least if $\vec v$ is really only a one dimensional parameter, measuring all the moments $\langle v^n \rangle_f$ seems to give me all the information to compute $\langle A \rangle_f$ with $A(v)$ ...
2answers
146 views

### Mathematical problems with impact on physics [closed]

Are there any purely mathematical, unsolved questions, whose resolution would have (great, or concrete) impact on physics? Eg. it could almost surely tell us whether particle x exist or not, assuming ...
0answers
115 views

### How is the poincare conjecture(and perelman proof) helpful in studying the properties of the universe?

Can someone tell me how the poincare's famous conjecture or its proof by perelmen can be helpful in deciding some properties like the shape of the universe?
4answers
477 views

### Topology needed for Differential Geometry [duplicate]

I am a physics undergrad, and need to study differential geometry ASAP to supplement my studies on solitons and instantons. How much topology do I need to know. I know some basic concepts reading from ...
3answers
316 views

### shifting from mathematics to physics

I am a postgraduate in mathematics. I studied physics during my B.Sc.studies.I want to go for further studies in physics particularly in theoretical physics. I am in a job and cant afford regular ...
2answers
342 views

### Book covering Topology required for physics and applications

I am a physics undergrad, and interested to learn Topology so far as it has use in Physics. Currently I am trying to study Topological solitons but bogged down by some topological concepts. I am not ...
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