Questions tagged [mathematical-physics]

DO NOT USE THIS TAG for elemetary physical questions. This tag is intended for questions on modern mathematical methods used in quantum theory, general relativity, string theory, integrable system etc at an advanced undergraduate or graduate level.

2,760 questions
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Catenary Cable Problem: Timoshenko (2 solvers since last year only)

I was doing this amazing problem Chapter 4, Problem 10 from book Engg Mechanics Revised 4E by Timoshenko, and here is the link having the modified problem which resembles a lot from book. ...
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Do infinity and zero really exist? [closed]

From the first day that I entered college, I was wondering about the relationship between some basic mathematical abstract concepts and nature. I'm going to explain them here and you may find them a ...
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Covariant derivative of a section of a trivial(?) associated bundle

First I'll briefly outline the physical context in which my question arose: If one tries to do 2D quantum mechanics in polar coordinates one encounters a problem with a property of the covariant ...
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Term for coordinate systems that are linear spaces with restricted set of symmetries

I'm trying to find a word or definition to capture something I've seen in theoretical physics. Physicists work with coordinate systems a lot, and they frequently represent physical facts as ...
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Maxwell Equation + initial data - dissipative or dispersive?

In Aspects of Symmetry, Coleman says (p. 185) ''Most of the simple field theories with which we are familiar have the property that all of their non-singular solutions of finite total energy are ...
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Find $\int_{0}^{\infty} e^{ix} \sin(x) \frac{e^{-3x}}{x} dx$

The second contribution in the Born approximation for the Yukawa potential in scattering theory leads to the following integral (for some given ratio of parameters): \begin{align} \int_{0}^{\infty} e^{...
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Path for fastest end velocity while accounting for friction

How would one calculate the path for the fastest velocity for a rolling object while accounting for frictions? Because ideally in the theoretical world, the path would not matter as long as there was ...
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What is this process/action called in English?

it is a fairly generate question regarding a terminology. People without science or engineering discipline makes an unfounded claim X, but people with such discipline start with proven facts A, B, C, ...
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What is the definition of a bounded operator in an infinite dimensional Hilbert Space?

I am struggling to understand the meaning of a bounded operator in a Hilbert Space. Does a bounded operator simply means that if it acts on an element of the Hilbert Space, the "result" is bounded?
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Application of representation theory

I often read that one can use representation theory in the field of quantum physics or for the analysis of symmetries in physics or chemistry. Unfortunately I coundn't find a concrete example for this....
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Meaning of the notation $L^2(\mathbb{R}^3)$ and its generalization

I'm not sure whether this question really belongs to this website. In quantum physics texts, and physics stackechange website, I have often seen the notation $L^2(\mathbb{R}^3)$. My glossary of ...
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Force is one form, but what does it mean to evaluate a force into a velocity?

I was reading an example from Lee's book to try understanding the two body problem (see below). Since the forces are conservative, there exists a $U : Q \to \mathbb{R}$ such that $F=dU$, so I ...
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Undetermined coefficients in a perturbative expansion

In order to familiarize myself with perturbation methods, I've been trying to derive the Lorentz transformations, given by \begin{align*} x \rightarrow \frac{x + vt}{\sqrt{1 - v^2}} & = (x + vt)(...
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Fisher Information in Statistical Mechanics

I am studying the canonical ensemble and it seems to me there is an analogy between derivatives of the partition function, which can extract energy momenta for the system and Fisher score /information....
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What makes the Cauchy principal value the “correct” value for a integral?

I haven't been able to find a good answer to this searching around online. There is a related old question here, but it never received much attention. Suppose I have some physical property that I ...
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Is there a way to mathematically prove $\psi (\mathbf{r})$ varies continuously (using the intuitive arguments provided below)?

Electric potential at a point outside the charge distribution is: $\displaystyle \psi (\mathbf{r})= \int_{V'} \dfrac{\rho (\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|} dV'$ where: $\mathbf{r}=(x,y,z)$ ...
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Derivative of Hankel functions and Bessel functions

Dose anyone know about the formulations of derivative of Bessel and Hankel function as below, because when I just used the derivative of Bessel function and Hankel function as in the following ...
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Author's derivation of time-independent form of Maxwell's equations

Laser Electronics, 3rd edition, by Joseph T. Verdeyen, gives the following: To describe an electromagnetic wave, we need two field-intensity vectors, $\mathbf{e}$ and $\mathbf{h}$, which are ...
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Is there a construction of the Wiener measure by discretization and limits which parallels the Physics ideas?

In Physics one constructs the path integral by a limiting process together with a discretization procedure. Now, in order to better paralell with the Wiener measure, consider this in Euclidean ...