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 ...

learn more… | top users | synonyms

0
votes
0answers
72 views

Is there an example where “filling in” a removable discontinuity produces a wrong result? [closed]

I am having an argument with a physics major. He claims that $\dfrac 00$ being undefined is just am inconsequential mathematical technicality. According to him, if we have an equation that describes ...
-1
votes
1answer
41 views

Why the function has to be a periodic function, if we want to find its Fourier series?

Why the function has to be a periodic function, if we want to find its Fourier series? What happens if the function has non-zero values over a finite range only? e.g. $ f(x) = e^{-x}; 0 \le x \le ...
4
votes
1answer
173 views

Why does math work for describing and solving physics problems? [closed]

The clarified version As far as I understand, Wigner considers a "miracle" the fact that it is even possible to find a mathematical equation that describes a natural phenomenon. It is not exactly ...
1
vote
0answers
289 views

Are all infinite sums not divergent? [migrated]

I recently came across a derivation of the infinite sum $1+1+1+1+..... $ that produced the result -1/2, aka zeta regularization (from Terry Tao's blog) This was quite surprising to me as I had ...
-1
votes
0answers
115 views

Does this divergent series appear anywhere in physics?

Question I recently managed to analytically continue certain divergent series. I was hoping if anyone could tell me if this expression appeared somewhere in physics: $$ \implies \lim_{k \to \infty} ...
2
votes
1answer
50 views

Nambu-Goto and Polyakov Actions

This might be a little bit of a technical question, so bear with me. Ok, so from string theory we know that the action for a relativistic string is found from the worldsheet when we embed the string ...
1
vote
1answer
73 views

Definition of winding numbers for Hamiltonian

In Witten's lectures at the PSSCMP/PiTP summer school, there is a use of winding number for "bad points" at sec.1.3. The formula is $$ w = \int_S\frac{d^2p}{4\pi}\left[\epsilon^{\mu\nu}\epsilon^{abc}...
1
vote
0answers
11 views

Proof from Calculus 1 [migrated]

Last days, from going into a website of the university of Pisa, I found an exercise given in the previous exams, in 1999. The problem was like: Given a continuous function f in R, and which ...
15
votes
4answers
719 views

Curvature of Hilbert space

That may appear as a dumb question, but: Does Hilbert space have curvature, or is it a flat space? How and why?
0
votes
0answers
31 views

What is the minimum math level required to comprehend general relativity? [duplicate]

I am currently working on a B.S. In chemistry and only need to go up to Calculus II, though I like to dabble in physics. What other math classes could I take to gain greater understanding of higher ...
2
votes
2answers
136 views

Physics without math [closed]

If anybody could imagine an advanced civilization with advanced knowledge of the universe(s) but without a mathematical language, how would they use their knowledge? How could it be possible to ...
-1
votes
2answers
45 views

General Approach and Intuition to Calculus based problems in Physics [closed]

I've done a calculus-based course in Mechanics, Electromagnetism and at the moment I'm studying Strengths of Materials. Time and again, one is faced with problems where Integration is used to sum up ...
0
votes
1answer
27 views

How to visualize this setup for deriving $\frac {dM}{dt}$ while water is evaporating

Establish a minuscule area dA on the interface and establish two angular coordinates. We measure the polar angle θ with respect to a line drawn perpendicular to dA and the azimuthal angle φ with ...
-1
votes
1answer
20 views

Why do proportionality constants come on only one side?

We know that voltage is directly proportional to current. Then if we change proportionality to equality, we get $V=IR$. Why not $I=RV$??
-1
votes
1answer
92 views

What kind mathematical Transformation is this?

$$\int f(\alpha)e^{\alpha^*y-z|\alpha|^2}\pi^{-1}~\mathrm d^2\alpha~=~z^{-1}f(z^{-1}y)$$ I am doing the problem of finding Wigner function for fock states given by the exercise problem from ...
0
votes
1answer
24 views

Is it correct to say that the constant of proportionality is proportional to the quantity itself?

So for instance, according to Newtons Law of cooling the rate of cooling is proportional to the temperature difference between the object and its surroundings. Mathematically $$\frac{dT}{dt}=-k(T-T_s)$...
0
votes
0answers
65 views

How to Solve this Integral

I am currently doing a problem in Quantum optics, specifically the problem of finding Wigner Function for Number states or Fock states. I am actually did the problem in a different way and found that ...
1
vote
1answer
115 views

Functional Analysis for Quantum Mechnanics [duplicate]

I have completed three sequences of courses in QM, and I'm very much eager to to do the functional analysis of QM on my own in my spare time. Can someone suggest some books? I like books with ...
3
votes
1answer
137 views

Is it possible to build a logical theory in QM based on quantum logic? [closed]

Quantum Probabilities as Bayesian Probability, Quantum probabilities as degrees of belief Above are two articles about quantum Bayesianism. I don't know why quantum Bayesianism use some results from ...
0
votes
0answers
23 views

Spivak for a soon to be undergrad. physics student [duplicate]

I'll soon start my undergrad. studies in physics and because of that I picked up Spivak's Calculus a while ago to get a solid foundation in single-variable calculus before I start my studies. However, ...
0
votes
1answer
67 views

Use of infinitesimals in physics [duplicate]

I want to ask about infinitesimals and non-standard analysis. In physics we always use $\mathrm dx,~\mathrm dv,~\mathrm dt$ etc. as infinitesimal quantities. When we deduce equations in physics, when ...
0
votes
0answers
24 views

Mathieu equation nonstable solutions

This israther mathematical question, but it is connected with some physics. Let's have Mathieu equation: $$ \tag 1 y''(t)+ (a -2q\cos(2t))y(t) = 0 $$ Suppose domain of parameters $a, q$ values, where $...
1
vote
0answers
58 views

How to calculate the contour integration with branch point? [closed]

The question come from a Mutusbara Sum like this $${ \sum _{ { z=i\omega }_{ n } } { \frac { -\alpha E\pi }{ 4{ z }^{ 3 }\sqrt { -\alpha -z } } } }$$ it equal a contour integral around Imaginary ...
0
votes
0answers
53 views

What knowledge do I need to learn Quantum Physics? [duplicate]

I have a quick question. What prior knowledge do I need to learn and understand quantum physics. For example, what type of math do I need to know, what level of physics, etc.
12
votes
2answers
1k views

Unfamiliar Notation in Sakurai

In chapter 5 section 9 of Sakurai, 2nd edition, he uses some notation that I am unfamiliar with. This may be suited for Math.se but I figured it could be peculiar physicist notation. Anyways it is ...
1
vote
0answers
47 views

What is a good mathematical introduction to QFT [duplicate]

I've noticed that, any time I try to pick up Peskin and Schroeder, the main stumbling block it the leap in mathematical constructs from QM. Is there a good textbook that could teach me some of the ...
2
votes
2answers
113 views

Is multiplication in physics purely mathematical or is there a physical explanation to it?

Here is what I mean: We always use mathematics in physics, which is pretty powerful, but I still need to ask whether multiplication in physics has a better explanation to what I already think. For ...
0
votes
1answer
74 views

Exact solution of Qubit Decoherence using Transfer Matrix

I'm going through a particular paper on decoherence: Exact Solution of Qubit Decoherence models by a transfer matrix method I'm having trouble understanding a particular step in the mathematics ...
3
votes
1answer
45 views

Derivative with respect to a difference of independent variables

I am dealing with an equation from nonlinear acoustics (Khokhlova-Zabolotskaya-Kuznetsov equation) where a strange term (for me as a mathematician) is used. The equation looks like this $$ \frac{\...
4
votes
1answer
104 views

Integrating elements of a Lie group with respect to parameters of the corresponding Lie algebra

I am working with an operator $\textbf{M}$ that is represented by the Lie group SO(1,3), thus it can be written as, $$ \textbf{M} = \exp{\textbf{L}} $$ where, $$ \textbf{L} = \begin{bmatrix} 0&a&...
1
vote
0answers
41 views

Relevance of pure mathematics vs statistics to physics [closed]

For someone currently studying physics, with an interest in experimental physics, would pure mathematics or statistics be more relevant?
5
votes
0answers
81 views

Mutual $E$ force due to charged coaxial rings [closed]

I found the following question in a good physics book I was solving and although this is a computer problem, I wonder if it can be done without using computers. $Q.$ Find the force of attraction ...
1
vote
0answers
44 views

Can someone help me to do the math? [duplicate]

This might seems off topic or something, but I am a middle school student and i'm really into Quantum Field Theory and String theory and every video on youtube or article on the internet shows only ...
1
vote
1answer
51 views

Book to study Dirac delta function from a physics point of view [duplicate]

I am a beginning physics graduate student. I am often bewildered by the strange properties of the Dirac delta function such as: $\delta (a x)= \frac{1}{a} \delta (x)$ The derivative of $\delta (x)$ ...
1
vote
0answers
23 views

Can you help me solve this using the current value Hamiltonian? [closed]

Okay, so I am getting a little stuck on this question, I will post it and then tell you how far I get. $$ max - \int_0^2 (x^2 + u^2)e^{-0.03t}dt\, $$ $$ x' = x-2u $$ $$ x(0) = 3 $$ $$ x(2)free $$ ...
20
votes
9answers
2k views

How to interpret the units of the dot or cross product of two vectors?

Suppose I have two vectors $a=\left(1,2,3\right)$ and $b=\left(4,5,6\right)$, both in meters. If I take their dot product with the algebraic definition, I get this: $$a \cdot b = 1\mathrm m \cdot 4\...
-1
votes
2answers
111 views

Disproving the mathematical universe hypothesis [closed]

The mathematical universe hypothesis is claimed by Lee Smolin to be falsifiable: [...] it is easy to disprove the mathematical-universe hypothesis. Simply exhibit one property of the natural world ...
2
votes
0answers
43 views

Seeking masters degree advice [closed]

I am graduating this semester with a bachelors in physics. My goal is to do theory in my graduate level course work. The problem I am in now is that I missed the deadline to take the physics GRE (I'm ...
0
votes
1answer
46 views

Assumptions in physics for Helmholtz decomposition

A version of the Helmholtz theorem says that, under opportune assumptions on the vector field $\boldsymbol{F}:\mathbb{R}^3\to\mathbb{R}^3$ and on $V\subset\mathbb{R}^3$ the following identity holds: $$...
1
vote
1answer
78 views

Why do people care about Mathieu groups and related things? (Something about monstrous moonshine)

Before I begin, let me say I don't know anything about what I am asking. This morning for somewhat random reasons I decided to google moonshine and related things. As it were I discovered my ignorance ...
3
votes
1answer
82 views

Existence and Uniqueness of Newton's Laws

I'm reading Arnold's book on classical mechanics. This is kind of a dumb question, but I'm having problems understanding his explanation for existence and uniqueness of Newton's laws. On page $8$ he ...
-2
votes
2answers
64 views

What Are Logarithms? [closed]

I'm just starting out and have a limited area of mathematic study and have no idea how to do logarithms. I know that they're involved in physics and want to progress. Could someone help?
0
votes
2answers
54 views

Can a laser beam be captured in prism?

is there a way to shoot a laser at a prism (or something) and have it glow when the laser hits it? I want to make a small box with a small hole in it. With the prism in the box, when the laser is ...
1
vote
0answers
59 views

Metric defining an sphere [closed]

I want to find for which cases this metric can define an sphere: $$\frac{1}{P^2}\left(\mathrm d\theta^2+\sin^2 \theta\; \mathrm d\phi^2\right)$$ where $P=\sin^2 \theta+K\cos^2 \theta$, with $K$ the ...
1
vote
3answers
90 views

Transition probability derivation

I have encountered this limit while learning time dependent perturbation and transition probability in Sakurai. How to show this limit? I tried to integrate around $x=0$ but didn't get anything useful?...
1
vote
0answers
61 views

Why is this differential added instead of subtracted?

I was looking at a derivation of the Barometric formula which reads like this: Consider a flat disc of air of mass $\mathrm{d}m$ at distance $h$ above the ground of mass $\mathrm{d}m$ and ...
3
votes
2answers
101 views

Proof that 1d lattice displacement by phonons is given $u_{n\pm 1}(t) = A_ke^{i\omega_k t} e^{i knd}e^{\pm i k d}$

I looked in «Kittel - Introduction to solid state physics», Wikipedia and Google for the derivation that: A phonon of wavenumber $k$ displaces the $s$-th atom in a monoatomic 1d crystal lattice by a ...
5
votes
1answer
82 views

Meaning of integral signs in classical physics

When I began studying physics, by myself, on a universitary textbook, F.J. Keller, W.E. Gettys , M.J. Skove, Physics, about one year ago, I believed that all the integrals that I was going to find in ...
-1
votes
1answer
54 views

Find the indicated quantities from the given data [closed]

This is a vector application. A rope is hung at both ends from a horizontal beam, and a weight m is suspended from it as shown in the figure. The left part of the rope exerts a force G at P, while ...
5
votes
2answers
478 views

Proof of Ampère's law from the Biot-Savart law for tridimensional current distributions

Let us assume the validity of the Biot-Savart law for a tridimensional distribution of current:$$\mathbf{B}(\mathbf{x})=\frac{\mu_0}{4\pi}\int_V \mathbf{J}(\mathbf{y})\times\frac{\mathbf{x}-\mathbf{y}}...