Questions tagged [physics]
Questions on the mathematics required to solve problems in physics. For questions from the field of mathematical physics use (mathematical-physics) tag instead.
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Meaning of $\int\mathop{}\!\mathrm{d}^4x$
What the following formula mean?
$$\int\mathop{}\!\mathrm{d}^4x$$
I know that this $\int f(x)\mathop{}\!\mathrm{d}x$ is the integral of the function $f$ over the $x$ variable, but the following $\...
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What is the relationship between the Boltzmann distribution and information theory?
I'm reading a paper on Boltzmann machines (a type of neural network in Machine Learning), and it mentions that "The Boltzmann distribution has some beautiful mathematical properties and it is ...
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Finding the radius of a neutron star that allows all points on its surface to be seen
At first glance, this fascinating question may seem better placed on Physics Stack Exchange. But, since I am only questioning the mathematics of the solution I decided it was more appropriate to place ...
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Show That A Particle In A Bounded Force Field Can Reach Any Point In Fixed Time Span
I tried to prove that for a smooth bounded force field $F$ and $x\in{\bf R}^n$ there exists some $v\in{\bf R}^n$ such that a particle starting in $0$ with mass $1$ and velocity $v$, obeying Newton's ...
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How to prove the derivative of position is velocity and of velocity is acceleration?
How has it been proven that the derivative of position is velocity and the derivative of velocity is acceleration? From Google searching, it seems that everyone just states it as fact without any ...
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Statistical Mechanics References
I need good references on the subject of Statistical Mechanics having a mathematically rigorous perspective.
Almost all physics books on this subject do not care about definitions/rigour/proofs etc. ...
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Applications of representation theory in physics
The notes of a lecture on basic group and representation theory I attended last semester begin with a bit of motivation for the argument. They give the following examples for applications in physics:
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Guide to mathematical physics?
I am currently a math phd student specializing in algebraic geometry aspiring to work at the boundaries of the the fields of mathematics and physics and so, was looking into the field of mathematical ...
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Wave-Particle Duality in PDE?
I am reading Arnold's Lectures on Partial Differential Equations. It is definitely a good book, yet sometimes I am a little bit confused.
One theme of the first chapter seems to be
From the ...
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Help to identify every equation in this meme? [closed]
A couple of the equations in this meme aren’t easy to read, and I probably don’t know them so I couldn’t tell what they are.
Can you identify all the equations, and help me feel smart on twitter?
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Is tossing of a coin deterministic experimemt?
This is a question that I practically encountered while I was playing a game:
Is tossing a coin a deterministic experiment?
It might seem silly to ask but I had some thought over it.
By the ...
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In what ways has physics spurred the invention of new mathematical tools?
I came across this comment:
Mathematical rigor is not a criterion that physicists have for evaluating their theories. From a mathematical perspective, the non-rigorous theories are far more ...
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Can Sturm-Liouville theory actually solve ODEs?
My teacher talked about Sturm-Liouville theory, and we learned that any second order differential equation can be put into the self-adjoint form. What is this? Well, the book says is something in the ...
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Solve functional equation $ h(y)+h^{-1}(y)=2y+y^2 $
I was trying to solve a certain physics problem, and encountered the functional equation that contains a function $h$ and its inverse $h^{-1}$:
\begin{equation}
h(y)+h^{-1}(y)=2y+y^2.\tag{1}
\end{...
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Energy functional in Poisson's equation: what physical interpretation?
Let's consider this boundary-value problem:
$$\begin{cases} -\Delta V = \rho & \rm{in}\ \Omega
\\
V=0 & \rm{on}\ \partial \Omega \end{cases}.$$
We know that this problem has a ...
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