"Mathematical physics consists of the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories." (from Journal of Mathematical Physics) This tag is intended for questions on methods used ...

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26 views

solving equation in terms of $w_1$ and $w_2$

I have a a physics problem involves the following equation $$\tan(\alpha) = \frac{(w_1 + w_2)^{1/2}}{w_3}$$ from a certain set of equations that I use I derive the following equation: ...
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2answers
53 views

Practical use for negative $dt.$

I am writing a section of notes for Calculus 1 on related rates. In the section where I discuss differentials, I write that the quantity $dt$ must be nonnegative. I imagined the only reason it would ...
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0answers
42 views

What's wrong with my math in this function to update the position of a planet near a star?

Initially the code seems to work as the planet curves toward the star, but then as it should either get pulled into the star or make an orbit, it just gets pushed away in the opposite direction. What ...
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1answer
23 views

Why is not parity transformation just a rotation?

I'm a bit confused about parity transformations (reflections). A parity operator $\pi$ takes a vector $(x, y, z)$ to $(-x, -y, -z)$. So in a $3$ dimensional space this takes a vector and points it ...
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36 views

Can someone help me to understand this formula.

Im trying to implement this in code, but I'm having some difficulties to understand it. • Using precalculation: $$\exp\left(-\frac{T}{T_f}\right) = 1 - \frac{T}{T_f} + ...
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18 views

Random walk problems [on hold]

What is the difference between restricted and unrestricted random walk in gamblers terminology?
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38 views

Problem of Arnold's book and covering spaces

I am currently reading Arnold's book "Mathematical Methods of classical mechanics" on page 278 and I don't see through his arguments there at a point. Especially, I am talking about the part that ...
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0answers
24 views

Particle on a hemisphere - lagrange

A particle of mass m is on top of a frictionless hemisphere centered at the origin with radius $R$. It starts sliding down the hemisphere. Set up the lagrange equatinos of the first kind and ...
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1answer
30 views

Connecting a mathematical solution to a differential equation with it's physical solution

I have seen this question in a neuroscience course: It is given after the lecture with these and these slides. I have no background in physics. However, I do know how to solve a differential ...
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1answer
62 views

Is there a physical interpretation of the alternating property?

A map from lists to list-elements is called "alternating" if any list with repeated elements is mapped to zero. This has statistical significance: regressions on collinear data are bad, dependent ...
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0answers
31 views

What math is needed for the inverse quantum problem?

What sort of mathematical background/familiarity is necessary and/or useful in tackling the inverse quantum problem? As an applied math major with a physics minor, I'm looking at different senior ...
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0answers
27 views

Interpretation of a certain transform

I'm having troubles with understanding the physical meaning of a certain transform. If $u$ is a solution to the wave equation $$\partial_t^2u-\Delta u=0\ \mathrm{in}\ ...
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0answers
10 views

Is the structure constant additive on connected components?

Definition of the Structure Constant Let $M$ be a Riemann surface and $\mu$ a smooth metric on it; let $\Delta_{\mu,\,M}$ be the Laplacian on $M$ induced by $\mu$ and ...
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1answer
54 views

Lagrange - motion

A particle of mass m is on top of a sphere of radius $R$. A small displacement makes the particle slide frictionlessly down the sphere. a)Set up the lagrange equations of the first kind for ...
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11 views

Oscillation - deflection from equilibrium state

A homogeneous, spherical electron cloud describes an atom (radius $a_0$ and total charge $^−e $ and positive point charge$^+e$ as the nucleus. An external electric field stimulates the electron ...
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2answers
65 views

Equations of motion - lagrange

A mass point of mass m moves on the circle $x^2+y^2=R^2$ and $z=0$. No external forces are acting. Solve the equation of motions and determine the constraint force with the lagrange equations of ...
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17 views

First representation theorem for sesquilinear forms - what is the role of the “core”?

In the first representation theorem, the notion of the core of a sesquilinear form appears. What is the intuition behind this notion, in context of this theorem and in general? I appreciate any ...
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1answer
30 views

Oscillation - atoms [closed]

A homogeneous, spherical electron cloud describes an atom (radius $a_0$ and total charge $^-e$ and positive point charge $^+e$ as the nucleus. An external electric field stimulates the electron ...
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1answer
33 views

Parabola Application [closed]

A cannonball when configured to be fired at a certain angle would have a parabolic path with a maximum height of $50\mathrm{m}$ and a horizontal range of $20\mathrm{m}$. If the cannonball is placed at ...
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3answers
67 views

How do one rigorously prove that the electric potential energy of an conducting sphere with charge $Q$ is $\frac{Q^2}{8\pi\epsilon_0R}$

How do one rigorously prove that the electric potential energy of an conducting sphere with charge $Q$ is $\frac{Q^2}{8\pi\epsilon_0R}$? Is integration the only way? Homogeneous charge distribution ...
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0answers
35 views

What curved ramp transports a ball from (1,1) to (0,0) most quickly, under the acceleration of gravity, with no friction or air resistance?

An infinitisemally small ball is placed at the top of a ramp which has a height of 1m and ends 1m away horizontally. What is the optimal curve of the ramp to minimize time taken for the ball to reach ...
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1answer
56 views

Electromagnetic tensor - I need help with a tensor calculation

First of all: this is not about the physics behind it. It's about the tensor calculation I've written down below. I know this kind of calculation is exhausting but I would be thankful if someone could ...
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40 views

How to prove and understand this result?

Suppose $(P,\pi, M)$ is a principal bundle with structure group $G$ and suppose $\omega \in \Omega^1(P,\mathfrak{g})$ is a connection on $P$ with curvature $\Omega = D\omega$. If $\sigma : U\subset M ...
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249 views

Arnold Trivium Problem 39

We find in Arnold's Trivium the following problem, numbered 39. (The double integral should have a circle through it, but the command /oiint does not work here.) Calculate the Gauss integral ...
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1answer
142 views

Damped Wave Problem

I understand what the general solution is to a wave equation, but am unsure of the general solution for a damped wave equation. If someone knows what that is, or the steps to find it, that would be ...
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1answer
34 views

Failing to calculate earth's standard gravitational parameter

I am using this equations from Wikipedia: $$\frac{4\pi^2 a^3}{T^2}=\mu$$ Where: $\mu$ = standard gravitational parameter ($\mbox{km}^3 \mbox{s}^{−2}$) $a$ = the orbiting body's semimajor axis (AU) ...
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1answer
31 views

Positivity of Coulomb energy for gerenal measures

Suppose $\nu$ is a compactly supported signed measure in $\mathbb R^{n\geq 3}$. Is the Coulomb energy still positive? More precisely $$\iint \frac{1}{\|x-y\|^{n-2}}d\nu(x)d\nu(y)\geq 0?$$ This ...
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32 views

Time period of oscillations of a point about the function's minimum value?

How am I to go about the following problem? Please do not explicitly solve it. Let $E_0$ be the value of the potential function at the minimum point $\xi$. Find the time period $T_0=\lim_{E\to ...
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0answers
26 views

Creating an arbitrary state of the quantum simple harmonic oscillator [migrated]

Suppose $\mathcal{B}=\{\lvert 0\rangle, \lvert 1\rangle, \lvert 2\rangle, ... \}$ is the energy eigen-basis of a quantum simple harmonic oscillator. I want to create the state \begin{equation} ...
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0answers
21 views

How to show that restricted Lorentz group (orthochoronous proper Lorentz transformations) is a normal subgroup?

Lorentz group is the group of linear transformations that leave the quadratic form $q(x_0, x_1, x_2, x_3) = -x_0^2 + x_1^2 + x_2^2 + x_3^2$ invariant. Linear transformations $A$ with $\det A = +1$ and ...
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1answer
39 views

Issues with solving PDE

It's been a while since I've had to solve the heat equation, and so I am having a slight issue. The question is as follows: A long, hollow, rigid tube, of length $L$ and constant cross section is ...
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8 views

How to solve the Helmholtz equation in a triangular region?

Suppose we take the Dirichlet boundary condition, namely the function must vanish on the boundary of the triangle. How about a general n-polygon?
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3answers
23 views

The magnitude of a triple product of two vectors

So I was going through a past exam for electrodynamics and a question for radiation came up and within it was the following magnitude of a triple product $ \lvert \hat{r} \times [\hat{r} \times ...
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1answer
24 views

Physics - Conservation of Energy problem with non earth object

A NASA satellite has just observed an asteroid that is on a collision course with the Earth. The asteroid has an estimated mass, based on its size, of 5×109kg. It is approaching the Earth on a head-on ...
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1answer
28 views

What is Fourier Transform of $\phi(x,y) = 2x $

How to calculate Fourier transform of this 2D function? $\phi(x,y)=2x$ for $-1<=x <= 1 ; and -1<=y<=1$ and $\phi(x,y)=0$ ; otherwise I tried like this: $\psi(u,v) = ...
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0answers
16 views

Quick question about the Frobenius method

When solving the the eigenvalue equation $\mathcal{L}\phi = E\phi$, where $\mathcal{L} = \left \{-\frac{d^2}{dx^2} + x^2 \right \}$ is a Sturm-Liouville operator, using the Frobenius Method $\phi = ...
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2answers
35 views

An object is already moving at 13 pixels/sec at t=0, and every second the speed decreases to..

An object is already moving at 13 pixels/sec at t=0, and every second the speed decreases to x=0.95 the speed at t-1. Once the object is going at a speed less than or equal to 1 pixel/sec it stops ...
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1answer
75 views

Path to understand the maths behind contemporary Physics.

I am a physicist but I do really love maths and I would like to learn and have a deep understanding of the maths used in theoretical physics, just for leisure, in my free time. I know there is a ...
6
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1answer
102 views

Why is the momentum a covector?

Can someone tell me why the momentum is an element of the cotangent space? More detailed: if we have some smooth manifold M and the cotangent space $T_{x}M^{*}$ I know that the momentum p is an ...
0
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1answer
30 views

Conservation of Kinetic Energy in Vlasov-Poisson System

I'm studying the very basics of kinetic theory in Vlasov Poisson Systems, and the first equation I'm studying is the free transport equation, i.e.: $$\frac{\partial f}{\partial ...
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0answers
16 views

Why $|j_1 - j_2 | \leq j \leq j_1 +j_2 $ holds for $J= J_1 +J_2 $, the addition of angular moment?

I wonder why the total angular momentum $$J=J_1 +J_2 $$ is given in the range of $$ |j_1 - j_2 | \leq j \leq j_1 +j_2 $$ Of course we can verify this in the course of finding Clebsh-Gordan ...
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2answers
82 views

What is the latest work being done in the field of Mathematics? 6/8/2015 [closed]

Young mathematics enthusiast here. I'm very curious to know what the top research is in the field of pure mathematics. Physics seems to take all the glory with quarks, then gravitons, Higgs ...
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1answer
34 views

What are the units of $\int_0^\infty \delta(x-x_0) \exp(-x/z)\; dx$, with $z$ in meters?

I am seeking to evaluate an integral of the form $\int_0^\infty f(x)\exp(\frac{-x}{z})dx$ where z has units of distance (meters) and f(x) is unitless. f(x) has two forms, as either a constant with ...
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0answers
21 views

logic verification angular momentum

So I have the following question: Your given a uniform right circular cone with a half angle at the apex of $\alpha$, a height of b and radius of $p_0$. Choose a coordinate system $O_{xyz}$ such that ...
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2answers
97 views

How to get the asymptotic form of this oscilatting integral?

So the integral is like this: $$\int_1^\infty \frac{\cos xt}{(x^2-1)\left[\left(\ln\left|\frac{1-x}{1+x}\right|\right)^2+\pi^2\right]}\mathrm{d}x$$ The question is how to get the asymptotic form of ...
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0answers
51 views

Axiomatising Physics

In problem number 6 of his famous list of 23 mathematical problems, David Hilbert asked for the axiomatisation of physics. My question is what does he really mean by that? Is not the problem solved by ...
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1answer
14 views

Moment of inertia tensor bounds

Can someone explain to me how did they determine the bounds in the following problem I did this in cylindrical coordinates but I would like to also understand this in order to fall back on cartesian ...
1
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1answer
29 views

Question about moment of inertia calculation and logic

Question: Determine the moment of inertia for a quadrant of a uniform circular lamina of radius b. Here I saw the answer that,however I don't understand it first of all here is the answer and I ...
2
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1answer
167 views

Explaining the differential operator found in Physics equations.

I'm new to this exchange so please bear with me regarding notation. I would like to know what the differential operator $d^n$ means as seen in some physics equations. Normally, one would have an ...
2
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1answer
34 views

Indices at the left of a tensor in mathematical physics/differential geometry?

I am a mathematician and I am reading a paper in mathematical physics and I found the following notation: Let $Y$ be a two–form on $M$ such that $$\nabla({}_iY_j)_k = 0.$$ Here, $\nabla$ is ...