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

-2
votes
0answers
35 views

Is this a good in introductory mathematics [on hold]

I have a question I was hoping to get some help answering. I have a I've read a few popular science books, but I want a deeper understanding than these books can provide. I think the next step for me ...
0
votes
0answers
21 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
53 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
50 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.
0
votes
0answers
19 views

How to make good approximation for a sum of squared expression? [migrated]

In both expression, n is integer and nmax is the maximum n and can be very large. How to use nmax to approximately and analytically to express these two expressiones? Are there any analytical ...
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 ...
-3
votes
0answers
81 views

What's the value of $\int f(x)\delta(x-a) dx$ if $a$ is not in the domain of integration? [migrated]

A problem occurs when I was solving an exersice of perturbative kind. The delta function has the fundamental property that \begin{align} \int_{-\infty}^{\infty}f(x)\delta(x-a)dx=f(a) \end{align} ...
1
vote
0answers
44 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
104 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
69 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
44 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 $$ ...
4
votes
1answer
103 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} ...
1
vote
0answers
39 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
79 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
47 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
20 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 ...
-1
votes
2answers
106 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
43 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
73 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
77 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
62 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
52 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
85 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 ...
1
vote
0answers
60 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
98 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
81 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
52 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
468 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 ...
10
votes
0answers
161 views

Reading differential forms

When, usually in text of physics or concerning thermodynamical aspects of chemistry, I find notations such as$$\mathrm{d}f=g\,\mathrm{d}t$$ I always interpretate it as ...
0
votes
1answer
66 views

Will Gödel's theorem strike a death blow to the future of science? [duplicate]

According to Gödel's incompleteness theorem, no matter how many statements you prove, you will always have a set of statements not proved. Does this imply that some time in the future, scientific ...
1
vote
0answers
60 views

Representing propagators as Dirac delta functions [closed]

I have found online, in particular on the wolfram site, http://mathworld.wolfram.com/DeltaFunction.html, certain identities that allow one to represent a delta function as limits. Of particular ...
9
votes
0answers
65 views

Experimental Hopf fibrations

Recently I read a paper where the authors experimentally constructed a Hopf fibration - that is, they created a quantum system where the nematic vector field of the system had a non-zero Hopf ...
1
vote
1answer
81 views

Does a continuum exist in reality? [closed]

There are uncountably infinite sets in mathematics. Such as the number of points in the interval [0,1] Or the set of all integer sequences. Do these have a physical reality? In case this helps : ...
1
vote
0answers
24 views

Calculating sieve screen size [closed]

I have a lot of mixed Lego, is it possible to calculate sieve screen dimensions to sort out particularly lego categories like bricks or plates ? So you can say if I use this screen size and ...
1
vote
2answers
65 views

Self similar functions

I'm trying to undestand the self-similarity as an invariance of a function under certain transformation. For example I think $$f(\lambda x)=\lambda^\epsilon f(x)$$ could be understood as a ...
1
vote
0answers
72 views

Intuitions for the simplest model in which the evolution of the laws of nature arises from the natural selection of structures [closed]

The problem I’m trying to solve can be described as To create the simplest model possible in which the evolution of the laws of nature arises from the natural selection of structures. This approach ...
1
vote
1answer
68 views

Problem arising from quantisation of e.m. field

In my studies on the quantisation of the electromagnetic field I've come across a small calculation that I wasn't able to reproduce. Remember the following: In the Gupta-Bleuler method to quantize ...
2
votes
0answers
55 views

Why are we allowed to decompose a function of two variables $f(x,y)$ into the form $\sum_n^\infty c_n(y)\psi_n(x)$? [duplicate]

I apologize if this is more mathematical than physical, but this issue always seems to come up when I am solving physics problems. Given a function of two variables $f(x,y)$ let us decompose it into ...
0
votes
0answers
47 views

Why do many equations need squared powers? [duplicate]

It seems that an equation factor must be “squared” as a convenient approximation to balance out some other series of factors invisibly . Might $E=mc^{1.95}$ work as well as $E=mc^2$? Might ...
2
votes
1answer
157 views

Are there any physical theories that use unsolved mathematics [closed]

In a talk Gödel and the End of Physics by Steven Hawking, he argues all mathematical problems are also physical problems for example: Given an even number of wood blocks, can you always divide them ...
1
vote
1answer
141 views

Why is the logarithm of the number of all possible states of a system differentiable?

Temperature of a system is defined as $$\left( \frac{\partial \ln(\Omega)}{ \partial E} \right)_{N, X_i} = \frac{1}{kT}$$ Where $\Omega$ is the number of all accessible states (ways) for the system. $ ...
1
vote
0answers
78 views

QFT and lack of rigour [duplicate]

How can physicists compute path integrals and such if there is no rigorous definition of it? If they can get an definite answer, there must be some method they used, so what is meant when ...
1
vote
0answers
57 views

Start learning Math for all my Physics [duplicate]

I know Physics but I don't know Math for this physics. Let me explain. When I say I know physics I mean I know stuff like Einsteins Special & General Relativity, Time Dilation, Gravitational ...
4
votes
0answers
77 views

Why are so many relationships in physics described by equations? [closed]

Consider $f$, some mapping between two ordered subsets of the natural numbers, $A$ and $B$. I see two ways $f$ can be expressed. The first way is an equation that defines $f$ (i.e. $f(A) = 2A$). ...
1
vote
1answer
83 views

Feynman's question on the mathematical machinery underlying nature [duplicate]

Physicist Richard Feynman said in his lectures "It always bothers me that according to the laws as we understand them today, it takes a computing machine an infinite number of logical ...
1
vote
1answer
140 views

$\pi$ and quantum mechanics [closed]

I read paper of Friedmann and Hagen Quantum Mechanical Derivation of the Wallis Formula for $\pi$ I am not a physicist but I know how to solve Schrödinger's differential equation for the hydrogen ...