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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Velocity needed for bullet to circumnavigate earth and land at our feet
Lets say we fire a bullet from a very powerful gun at a height of 1 metre parallel to the surface of the Earth. Assume there is no air resistance and the only force acting on the bullet is from Earth'...
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Residue of $z^2 e^{1/\sin z}$ at $z=\pi$
A while back I was working through many problems in Mathews and Walker's Mathematical Methods of Physics. In the appendix is this problem:
A-6. Find the residue of the function $z^2 e^{1/\sin z}$ ...
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Property of Dirac delta function in $\mathbb{R}^n$
How does one prove the following identity?
$$\int _Vf(\pmb{r})\delta (g(\pmb{r})) \, d\pmb{r}=\int_S \frac{f(\pmb{r})}{\left|\operatorname{grad} g(\pmb{r})\right|} \, d\sigma$$
where $S$ is the ...
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Quantum mechanics for mathematicians
I'm looking for books about quantum mechanics (or related fields) that are written for mathematicians or are more mathematically inclined.
Of course, the field is very big so I'm in particular ...
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A simple geometric problem, solving $f'(x)=\frac{f(x)}{\sqrt{r(x)^2-f(x)^2}}$, given $r(x)$.
Introduction
Suppose we have a convex, real function $f(x)$. We can define a tangent line to this function $t(x,s)$. Then, we can find the intersection of $t(x,s)$ with the $x$ axis. Let's call this ...
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Guidance regarding research in Mathematical Physics
I am currently a Master's student in Mathematics. The main focus of my undergraduate programme was on Mathematics. However as a part of the course, I have done some Theoretical Physics courses. In ...
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Angular distribution of lines passing through two squares.
Let's say I've got two squares with side length $d$ that are held parallel at a distance $m$ apart.
Suppose that particles are randomly falling from above in such a way that the polar angle $\...
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Publication date of the book of Michael Spivak - Physics for Mathematicians II?
I bought the book "Physics for Mathematicians I" by Michael Spivak (http://www.amazon.com/Physics-Mathematicians-Mechanics-Michael-Spivak/dp/0914098322), have worked through quite some ...
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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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Can this gravitational field differential equation be solved, or does it not show what I intended?
This is the equation I'm having trouble with:
$$G \frac{M m}{r^2} = m \frac{d^2 r}{dt^2}$$
That's the non-vector form of the universal law of gravitation on the left and Newton's second law of ...
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Quantum mechanical books for mathematicians
I'm a mathematician. I have good knowledge of superior analysis, distribution theory, Hilbert spaces, Sobolev spaces, and applications to PDE theory. I also have good knowledge of differential ...
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What is the optimum angle of projection when throwing a stone off a cliff?
You are standing on a cliff at a height $h$ above the sea. You are capable of throwing a stone with velocity $v$ at any angle $a$ between horizontal and vertical. What is the value of $a$ when the ...
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How to introduce stress tensor on manifolds?
I want to understand the type of stress tensor $\mathbf{P}$ in classical physics.
Usually in physics it is said that the force $\text d \boldsymbol F$ (vector) acting on an infinitesimal area $\text ...
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What is the moment of inertia of a Gosper island?
We know that regular hexagons can tile the plane but not in a self-similar fashion. However we can construct a fractal known as a Gosper island, that has the same area as the hexagon but has the ...
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The vertices of an equilateral triangle are shrinking towards each other
For an equilateral triangle ABC of side $a$ vertex A is always moving in the direction of vertex B, which is always moving the direction of vertex C, which is always moving in the direction of vertex ...
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