Tagged Questions

"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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2answers
25 views

Greens function method for Newtonian potential

this may be a silly question but, well you know when solving for the Poisson equation that gives the Newtonian potential, $\Phi$, (for a point mass, $M$, at the origin) $$\nabla^2 \Phi = 4\pi G ...
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0answers
6 views

abel transform on a 3-d gaussian [on hold]

I have been trying to do an Abel transform on a 3-dimensional Gaussian function. But I'm not clear about certain points. I would like to see a solution step by step, with each integral evaluated ...
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0answers
47 views

Sorting out some integrals from physics

I'm doing some physics for a change, and I'm trying to sort things out a bit. From the definitions of mass, torque, momentum and angular momentum I've come up with the following integrals: ...
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0answers
19 views

Solving a PDE via method of characteristics

I'm interested in solving the following PDE via the method of characteristics: $$\frac{\partial f}{\partial t} - ax\frac{\partial f}{\partial p}+ bp \frac{\partial f}{\partial x} = 0,$$ with ...
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0answers
23 views

Show the conditions for circular orbit

I am working through this exam practice question, and just need a bit of guidance with the last few parts, would greatly appreciate any help: The relativistic Lagrangian to describe the hydrogen atom ...
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0answers
22 views

WKB approximation for multiple turning points

I'm working on a numerical program which approximates the eigenvalues of a Schrödinger equation by making use of the WKB approximation formulas. For example, if the Schrödinger equation is $$ y''(x) = ...
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0answers
14 views

Questions about the formula for inductive reactance and $Z_t$

I am currently on the inductors unit in my Navy schooling and I have two questions about these formulas that I learned about. As I'm aware, the ability of an inductor to concentrate a magnetic field ...
2
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2answers
55 views

Quaternion - Spinor relationship?

I've known for some time about the rotation group action of the ('pure') quaternions on $ \mathbf{R}^3 $ by conjugation. I've recently encountered spinors and notice similarities in their definitions ...
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1answer
26 views

How do I find the relative coordinates of a picture of a plane in 3d space.

I have a box, with corners $A$ through $H$, as depicted above. I'll consider $B$ the origin of a coordinate system, with the $x$ axis in the direction through $C$, the $y$ axis through $A$ and the ...
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1answer
33 views

Discovering the mathematical nature of Nature - Galileo's inclined plane experiment

In 1638 Galileo published Two New Sciences, in which he described his inclined plane experiment. He discovered that the acceleration of gravity was uniform, and could be modeled mathematically by the ...
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0answers
29 views

Convert time derivative to a function of time

Physics: I am asking for help to derive a general expression for the total amount of energy lost as a function of time from a radiating object. I'll simplify my problem like this: Say for example ...
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1answer
31 views

Analytical solution for bound state energies of infinite well

I am trying to find bound state energies assuming infinite potential. I have been told it can be done by analytically solving Right Hand Side and Left Hand Side of an equation such as: ...
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1answer
20 views

Projectile Motion using cos and sin theta???

Golfball is struck to clear a tree 20m away and 6m high at an angle of elevation of 40degrees. Find the speed of the ball when it leaves the ground. I've created my displacement equation with i and j ...
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0answers
17 views

identity of equation

We have the equation ($\partial_{\mu}\partial_{\nu}$-$\eta_{\mu\nu}\Box$)$\phi=0$, where $\phi$ is a scalar field, $\Box=\partial_{\mu}\partial^{\mu}$ is a standart Dalamber operator, $\eta_{\mu\nu}$ ...
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1answer
25 views

arrange m balls in to n baskets

How can I write a given natural number into sum of required (m) natural numbers? Example: 10=2+8+0 here m=3 Let n_i be the values i:e 2,8,0 in the above example. I want to know whether any method ...
1
vote
1answer
18 views

Nested square brackets in tensor indices

I know that using square brackets on tensor indicies denote the anti-symmetric part $$ T_{[ab]} = \frac{1}{2} \left( T_{ab} - T_{ba} \right)$$ I now have to prove that $$ T_{a [[bc]d]} = T_{a ...
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0answers
15 views

Zeta function and heat kernel

It is easy to prove that zeta function $$\zeta_{\Lambda}(s)=\sum \frac{1}{\lambda_{n}^{s}}$$ and trace of heat kernel $$K_{\Lambda}(t)=\sum e^{-\lambda_{n}t}$$ satisfy the relashion ...
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1answer
47 views

boundary conditions for operator

if you have a Schrödinger operator on a sphere ( $\mathbb{S}^2$) $-\Delta_{\theta,\phi} \psi(\theta,\phi) + V(\theta) \psi(\theta,\phi) = E\psi(\theta,\phi),$ where the potential does not depend on ...
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0answers
33 views

Laplacian on $\mathbb{S}^2$ has a pure point spectrum

Consider an operator $T = -\Delta + V(\theta)$ where $V(\theta)$ is $C^{\infty}$ and $T : C^{\infty}(\mathbb{S}^2) \subset L^2(\mathbb{S}^2)\rightarrow C^{\infty}(\mathbb{S}^2).$ I was wondering why ...
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0answers
31 views

How to calculate Hill's discriminant?

I am currently reading this paper on Schrödinger operators see here. On page 6 and 7 they talk about Hill's discriminant and how this is connected with the spectral properties. They also show some ...
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0answers
13 views

Rotation about an axis by matrix multiplication

Suppose I have three axis of rotation vectors $\vec{v_1},\vec{v_2},\vec{v_3}$ and angle of rotation as vectors $\theta_1,\theta_2,\theta_3$. Take a vector $P$ then apply rotation around $\vec{v_1}$ ...
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1answer
22 views

how to calculate the phase shift in the formula that has sin in both side?

Given formula $asin ( x ) = b sin( x + \phi)$ where $a$ and $b$ are constants. I want to calculate $\phi$.
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0answers
22 views

Quaternion - An equivalent form

Given Data in the problem I have rotation matrices represented by a quaternion $q(t)$ and we are aware of axis of rotation at each point as $\psi(t)$ and angle of rotation $\theta(t)$. I have a ...
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0answers
12 views

How could one go about constructing this relatively simple contagious diffusion-reaction model?

How could one go about constructing a contagious diffusion-reaction model showing the relationship between disease (e.g. Ebola) and number of available healthcare workers in an unevenly distributed ...
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votes
1answer
26 views

physical meaning of heat equation

consider the heat equation $u_t=a(t)u_{xx}+f(x,t)$, $0<x<L$, $0<t<T$ subject to the initial condition $u(x,0)=g(x)$ and boundary conditions $u(1,t)=0,$ $u_x(0,t)+hu(0,t)=0$ where ...
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0answers
47 views

Proof of Kepler's first law

Has Kepler ever provided proof of his first law? I've found some articles on the web which use some of the Newton's formulas to prove it but Kepler died before Newton was born. So how did Kepler ...
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1answer
45 views

What happens when this turns to $dx$?

I have this equation: $$ ds^2=c^2dt^2-dx^2-dy^2-dz^2. $$ And I've also been given $$ x=x'\cos(\Omega t)-y'\sin(\Omega t), $$ which I need to substitute into the first equation. I've squared $x$ to get ...
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1answer
41 views

Why is $\int_{\mathbb{R}^3} |p\rangle \langle p| d\lambda(p)=id$?

As I have written in the headline, I am curious how the relation $\int_{\mathbb{R}^3} |p \rangle \langle p| d\lambda(p)=id$ that physicists use, where $|p\rangle$ is the eigenfunction to the ...
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0answers
14 views

The variational bicomplex with dependent fields

I would like to understand a certain approach to variational problems that I've seen in the physics literature. In particular, I'd like to express it in terms of the variational bicomplex. However, ...
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0answers
14 views

k-space tensor integral in statistical mechanics [duplicate]

k is the modulus of the vector k. Please help me to integrate the above tensor expression in the infinite domain of the vector k. I have tried to let u in the direction of kz and then transform the ...
1
vote
1answer
34 views

$k$-space tensor integral in statistical physics

$$Q=\int_{\text{all space}} \frac{\hbar \nu_g \mathbf{k}\mathbf{k}}{\exp[(\hbar \nu_g |\mathbf{k}|-\mathbf{k}\cdot\mathbf{u})/k_B T]-1}d\mathbf{k} $$ Please help me to integrate the above tensor ...
1
vote
2answers
46 views

Damped simple harmonic oscillator, phase space

I want to calculate and draw the phase space trajectory of this damped harmonic oscillator: $$\ddot{x}+\gamma\,\dot{x}+\omega^2x=0$$ for the two cases $\gamma=2\omega$ and $\gamma=\omega$. I'm ...
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1answer
25 views

Clarifying understanding of Poisson Brackets in Hamiltonian Dynamics

I'm just reading through my textbook and would like to clarify my understanding of 'Canonically related variables'. In my textbook, it says that if $Q_i$, $P_i$ are related to $q_i$, $p_i$ by a ...
1
vote
1answer
135 views

Newton's Law of Cooling, age of Earth, weak math skills

I'm curious about a problem concerning the age of the earth, but I don't have the math skills to think properly about it. I've found the solution to Newton's Law of Cooling, and I can handle that ...
2
votes
1answer
57 views

question about monoidal structure of a 2-category

Consider an extension of the 1-category of vector spaces and linear maps down to a 2-category $\mathcal{C}$ whose objects are $k$-linear categories. What is the symmetric monoidal structure on the ...
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0answers
21 views

Momentum Representation vs Position Representation

I have a question involving the representation of operators in momentum representation and position representation. The question is a little long, so I'll do my best to explain it. We are given an ...
0
votes
1answer
38 views

Convert coordinates to a different coordinate axis

Sorry for any forum rules I have broken, I needed a quick answer. I want to create a plane including 3 nonlinear points on a 3d coordinate system, one being the origin. I also need to create a ...
2
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0answers
98 views

Learning Roadmap to Mathematical Physics

Currently, I am a graduate student specializing in algebraic geometry. On the other hand, I have also become extremely interested in the mathematical physics. However, I am not sure what steps I ...
0
votes
1answer
37 views

Calculating the electric field of a disk

I'm having trouble regarding how to calculate the electric field of a disk. Here's the scheme: The exercise states that the disk is uniformely charged. This is what I did: Density charge : ...
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1answer
35 views

Inverse laplace transform in a physics problem.

This came up during a physics problem, where we need to find the inverse laplace transform of $$X(s) = \left( 1+ \frac{k}{ms^{3/2}}\right)^{-1} \left( \frac{c_1}{s^2} + \frac{c_2}{s} \right)$$ to ...
4
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0answers
248 views

Explain this step in lecture notes

The bounty offered is for the person that explains me how the author gets from equation 3.19 to equation 3.20 in these lecture see here. Normally I would agree that copying the relevant equation would ...
0
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0answers
8 views

Analytic Continuation of Fourier Transform to a Strip in Complex Domain

This is to prove Theorem IX.13 from the Methods of Modern Mathematical Physics (by Reed & Simon). Let $f$ be in $L^2 (\mathbb{R}^n)$. Then $e^{b|x|} f \in L^2(\mathbb{R}^n)$ for all $b<a$, if ...
5
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1answer
103 views

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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0answers
21 views

Cancellation of dots lemma (Lagrange's equations)

Derivations of the Lagrange's equations introduce at some point the "cancellation of dots lemma", \begin{equation} \frac{\partial \mathbf{r}}{\partial q_{i}} = \frac{\partial ...
0
votes
2answers
95 views

Linear algebra too early.

I have started college few days ago. At the first exposition of physics, professor has been reminding us what is vector and what is definition of a vector. But he has been using linear algebra to ...
3
votes
2answers
23 views

Mathematical expression for map from $[0,1]$ to $S^2$

A topological space is called arcwise connected if, for any points $x,y\in X$, there exists a continuous map $f: [0,1]\rightarrow X$ such that $f(0)=x$ and $f(1)=y$. Although it is intuitively ...
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3answers
47 views

Connectedness of $O(3)$ group manifold

A topological space is said to be connected if it cannot be written as $X=X_1\cup X_2$, where $X_1,X_2$ are both open and $X_1\cap X_2=\emptyset$. Otherwise, X is called disconnected. Is it wrong to ...
1
vote
1answer
68 views

how to solve the system of differential equations for this particle?

I'm trying to solve this problem A particle of mass m moves under the action of gravity on the inner surface of a paraboloid of revolution $x^2+y^2=az$ which assumed frictionless. Obtain the ...
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0answers
21 views

Explain why we describe the flow of fluid passing through volume with this equation

I am new to this Q&A site. Recently I came across this expression while watching a video http://www.youtube.com/watch?v=GveJWPr9UOk/ about the mass of fluid flowing in through a cube. You can find ...
10
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1answer
175 views

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 8 Theoretical Physics courses(2 courses ...