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Questions tagged [mathematics]

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 curriculum, such as, e.g., number theory, category theory, algebraic geometry, general topology, algebraic topology, etc.

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6 views

Can roots be $y$-intercepts of the quadratic function [migrated]

I know this must be stupid question, but I was wondering why cannot a quadratic or any polynomial equaiton be in format of and to find roots we set y=0. In short,, does y intercept can also be roots ...
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0answers
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1answer
72 views

Distance from ground to start suicide burn with initial height

In the figure below, the rocket is dropped with no initial velocity at a height of $h$. $d_f$ (free fall distance) is the distance in which the rocket is in free fall. $v_b$ is the velocity due to ...
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3answers
111 views

Why do my books introduce the equation $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$ without showing partial derivatives of $\mathbf{E}$ exist?

In electromagnetism (electrostatics), we often come across the equation $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$. In order for this equation to be meaningful, $\mathbf{E}$ must be a ...
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0answers
20 views

Lagrange Multiplier with inequality conditions

How can Lagrange multiplier method be used when inequality conditions are given instead of equality conditions?
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0answers
59 views

Generalisation of finite to infinite vector space [closed]

To generalise finite vector space into infinite vector space..this book(principle of quantum mechanics) says we redifine inner product of 〈f|g〉as [ limit n tends to infinity Σfₙ(xᵢ).gₙ(xᵢ)Δ ]where ...
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0answers
25 views

Variational Problem with Variable Endpoint [closed]

I'm struggling with the general derivation of the transversality condition for a variational problem for some functional $\phi (x,y(x),y'(x)$, where the initial point is fixed, but the final point is ...
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0answers
16 views

Mathematical bases/prerequisites for Feynman's “QED” [duplicate]

I have enjoyed studying Feynman's book "QED". I have sufficient mathematical maturity to go beyond his analogies. I am hoping someone has provided notes on the book enumerating the mathematical basis ...
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0answers
17 views

Isomorphism between functions [closed]

Is there an intuitively achievable isomorphism between the functions of a component in $3N$ variables (for example, in a configuaration space of $N$ particles in a three-dimensional physical space) ...
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0answers
46 views

Coordinate transformations [migrated]

I have two scalar functions of $x$ and $y$ that I can define: $$f(x,y)=x^2+y^2\qquad \text{and}\qquad g(x,y)=x^2 + \sin^2(x) y^2.$$ Is it true that there is literally no coordinate change that will ...
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7answers
8k views

Why does Taylor’s series “work”?

I am an undergraduate Physics student completing my first year shortly. The following question is based on the physical systems I’ve encountered so far. (We mostly did Newtonian mechanics.) In all of ...
2
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0answers
50 views

The derivative of the Delta function times another function [migrated]

Good evening! I can't understand how to prove that $$\alpha(x)\delta'(x)=-\alpha'(0)\delta(x)+\alpha(0)\delta'(x).$$ I tried to use $$(Df,\phi)=-(f, D\phi),$$ also I used that $$(D(hf),\phi)=(h'f+hf',\...
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1answer
27 views

Why is force 0 either side of an inflexion point in neutral equilibrium?

In Tipler & Mosca 5th edition p173 it defines neutral equilibrium as a point in a U-x curve where $\frac{dU}{dx}=0$ and also $\frac{dU}{dx}=0$ for a small displacement either side of the point. ...
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11answers
1k views

Is there a proof that the set of real numbers can exactly represent distances? [duplicate]

Mathematicians define real numbers in an abstract way - as an 'ordered field' with 'the least upper bound property'. In physics, we use real numbers to represent distances. For us to be able to do ...
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0answers
72 views

Why isn't the scalar product of a covector and vector symmetric? [migrated]

In tensor math, how come the scalar product of a co-vector (co-variant vector) with contra-variant vector, as written between angle bracket separated by comma, $\langle x, a \rangle$, is not symmetric?...
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3answers
57 views

How to derive kinematics equations using calculus? [closed]

I read derivation of kinematics equations using calculus: $$a=\frac{\text dv}{\text dt}$$ $$\implies \text dv=a\text dt$$ $$\implies \int_{v_0}^v\text dv=\int_0^t a\text dt$$ $$\implies v-v_0=at$$ $$\...
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1answer
36 views

Derivative of tensor product of quantum states

Recently I asked a question over at the math stack exchange: https://math.stackexchange.com/q/3210375/. However I figured I'd ask here too, seeing as the question originated in a physics course I'm ...
2
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2answers
90 views

Infinite sum: Renormalisation

Trying to do the calculation made in a physics article Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling (page 10 to go from equation 56 to 57), I ...
3
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0answers
73 views

Characteristics of the Navier-Stokes equations as a set of PDE's

I am not entirely sure if I should ask this question here or not, but here goes: can anyone suggest any reference (book, article, etc.) about the Navier-Stokes equations from a mathematical point view?...
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0answers
20 views

Which books or content should I prefer to understand particle physics operator and representations [duplicate]

I am just a intermediate passout and I want to know which books should I prefer for learning the mathematics of particle physics level like the different representation, operation like Hamiltonian, ...
0
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1answer
46 views

Is curvature the exterior covariant derivative of the connection?

Let $P\to M$ be a $G$-principal bundle, $G$ a topological group, $\omega$ the connection and $V$ a vector space. We define $d_\omega: \Omega^k_G(P, V)\to\Omega^{k+1}_G(P, V)$ the exterior covariant ...
3
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2answers
114 views

Precise definition of the Hilbert space in QM?

In QM books (at least those I have read) the definition of the Hilbert space used is somewhat blurred (the "space of square integrable functions" is not enough to define it precisely : which kind of ...
2
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2answers
290 views

Does it make sense to speak in a total derivative of a functional? Part I

I would like to consider the problem of the total derivative of a given functional \begin{equation} \mathcal{L}\bigg[\phi\big(x,y,z,t\big),\frac{\partial{\phi}}{\partial{x}}\big(x,y,z,t\big),\frac{\...
1
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1answer
78 views

Dirac delta function mathematical expression proof

In a discussion of the second order transitions in graphene this mathematical expression is used. $$ \left|\frac{1}{\varepsilon + i \Gamma/2}\right|^2 = \frac{2\pi}{\Gamma}\delta(\epsilon) $$ And I'm ...
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1answer
89 views

Is math truly infinite or is it just theory? [closed]

I imagine you can theoretically add +1 to any number But untill it happens it isnt so. That + no free will = math is limited and has a definite value. I imagine its tied in with conservation laws... ...
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0answers
40 views

How to prove that the limit of surface integral exists?

My book "Electromagnetic Fields" says in $\text{Section}\ 3.4$: Question Why does the limit in equation $(3.42)$ exist (convergent)? Why is the contribution from $(S-S_{\delta})$ remains ...
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0answers
36 views

A. Zee Contour Integral

In A.Zee's book I have come a cross an integral which I found difficult to solve.
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2answers
81 views

What are the theorems that constitute the Maxwell's equation? [closed]

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
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2answers
110 views

Non-rigorous math books [duplicate]

I’m self-studying physics and mathematics out of interest and I am looking for some non-rigorous (text)books on mathematics. Perhaps one book covering all areas relevant to physics or separate books ...
3
votes
1answer
69 views

Diffusion equation with time-dependent boundary condition

I was trying to solve this 1D diffusion problem \begin{equation} \dfrac{\partial^2 T}{\partial \xi^2} = \dfrac{1}{\kappa_S}\dfrac{\partial T}{\partial t}\, , \label{eq_diff_xi} \end{equation} with ...
0
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1answer
72 views

Do non-abelian group mathematics have any use in the real world math? [closed]

I know physics uses a lot of non-abelian mathematics (though I cannot wrap my head around ab does not equal ba).. Is there any real world (macro world we live in) uses for non-abelian mathematics? ...
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0answers
35 views

Is there an easier guide or something to George Arfken's mathematical methods for physicists? [duplicate]

I'm doing bachelor's in Physics and in 3rd semester the professor introduced Mathematical methods with us, which seemed like a great book at first but by the time we started a chapter on Tensor ...
3
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2answers
114 views

Complex conjugated representation and its Young tableaux

This post is an exact copy of one that I posted in Math's site. I do this copy because people there suggested me to do it since, apparentely, in Mathematics and Physics we use different conventions ...
4
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0answers
76 views

Why do we assume wavefunctions to be finite and continuous everywhere? [duplicate]

Why do we assume the wavefunctions to be everywhere finite and continuous? Finiteness maybe required due to square integrability but why continuous? Such a restriction is not imposed on its derivative....
2
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0answers
94 views

Euler-Maclaurin formula for path integral

Is there a corresponding Euler-Maclaurin formula for path integral when we divide the path integral into discrete lattice? What is the error correction when we divide the space into lattice of length ...
2
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1answer
78 views

Fourier transform property in Feynman 1986 Dirac Memorial Lecture

In his famous 1986 Dirac Memorial Lecture, Feynman refers to a Fourier transforms theorem holding in case F(w) satisfies "certain properties", while being restricted to positive frequencies only: ...
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1answer
50 views

Fourier transform of derivative of plane wave [closed]

What is the Fourier transform $F(k)$ of: $$ f(y) = A \, ik \, e^{iky} $$ If you calculate it with Wolfram Alpha, it says that there are no results found in terms of standard functions.
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1answer
33 views

Need some help to show this relationship using parseval's theorem [closed]

Use Parseval’s theorem for the Fourier series and take L → ∞ to show that:
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2answers
98 views

Can we create new physics through moderately brute force computing? [closed]

So my argument for this is that the expansion of knowledge in any field of physics depends on what is previously known, and what we physicists express or knowledge as equations. So here's what I ...
1
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1answer
83 views

Representing a reducible Cartesian tensor as a spherical tensor

I'm quite confused by this transformation, and am trying to gain fluency in moving back and forth between these objects. I understand that a second order dyadic Cartesian tensor can be represented as ...
0
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0answers
28 views

Rigorous Treatment of Quantum Tensor Operators

Recently, my classes have introduced me to the idea of spherical tensors and the Wigner-Eckart (WE) Theorem, but my previous classes on tensors had emphasis on things like covariance, contravariance, ...
1
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1answer
38 views

Electric Flux of A Point Charge Derivation

I am trying to understand the derivation of Gauss's Law and came across this line describing the electric flux through a small area of a sphere from a point charge: Source $$ E\cdot\Delta A_i = E_n\...
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1answer
74 views

Mathematics textbooks to understand Jackson electrodynamics

I want a very solid mathematics background that will make going through Jackson's text less challenging. What books would you recommend?
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1answer
33 views

Electric field on the boundary of a continuous charge distribution

In Purcell and Morin's Electricity and Magnetism, 3rd Edition, the claim is made that the magnitude of the electric field on the boundary of a continuous charge distribution is finite (assuming the ...
11
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7answers
939 views

Can we divide a vector by another vector? How about this: $a = vdv/dx?$

My physics teacher told us that we can’t divide vectors, that vector division has no physical meaning or significance. How about this: $$a = vdv/dx.$$ It says acceleration vector equals velocity (as ...
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1answer
69 views

Is it necessary to learn complex analysis in order to learn classical electrodynamics?

I am reading "Classical electricity and magnetism, chapter 1" by Wolfgang K. H. Panofsky and Melba Phillips. I am having little trouble on page 13 and afterwards. It talks about singularity, poles, $2^...
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0answers
30 views

Relation between computation of curl and divergence and their formal definitions

both divergence and curl of a vector field have a formal definition, however, we don't use these definitions when we compute the divergence or curl. so can we just derive the computations from the ...
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votes
2answers
74 views

Is gravitational constant a rational number? [duplicate]

The question is the title. But I'm quite doubtful if this question is meaningful or not. Since this constant is obtained by experiment, we can never know its exact value, unlike $π$ or $e$. Is it ...
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0answers
70 views

What optical system could perform a multiplication/convolution of several rectangular pulses with different widths?

Statement There is a following multiplication/convolution of $n$ rectangular pulses with different widths $$ f(x)=\mathrm{rect}(c_1x)\ast\mathrm{rect}(c_2x)\ast\ldots\ast\mathrm{rect}(c_mx) $$ or $$ ...
1
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0answers
81 views

Pure math courses for physicists: Topology [closed]

I'm in my bachelor in physics. In a couple of weeks I start my last year, and I'm interested in taking some pure math courses. As you see, I like the theoretical point of view, but I don't know if the ...