"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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5
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1answer
609 views

Cylinder-ray intersections equation

I found an article involving infinite cylinder-ray intersections, and I don't know how they develop this equation: $$(q - p_a - (v_a, q - p_a)v_a)^2 - r^2 = 0$$ In the end of the first page I quote: ...
-4
votes
0answers
62 views

Path integrals in mathematics [on hold]

I was wondering if there are any applications of path integrals in mathematics? Can it be used to prove anything?
-4
votes
1answer
29 views

Electrostatics: Application of Coulomb's Law [on hold]

Two small sphere are both positively charged and carry charges of 8 micro Columbus and 18 micro Columbus respectively. Their centers are 20 cm apart. Find the location of the point between them at ...
0
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0answers
15 views

Vector diagram: forces

Using a vector diagram,explain why it is easier to do chin ups when your hands are 30cm apart instead of 90 cm apart.(Assume that force exerted by your arms is the same in both cases). If someone ...
0
votes
1answer
36 views

Difference between position vector and distance vector? [on hold]

Its similarities and dissimilarities between position vector and distance vector?
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1answer
30 views

Scalar property of $ C(\Omega)=\sum_{|\alpha|\leq m}\color{blue}{\big|\Omega\big|^{\dfrac{2|\alpha|-n}{n}}} \int_{\Omega}|D^\alpha f|^2\ dx $

This is closely related to a previous question: Scale invariant definition of the Sobolev norm $\|\|_{m,\Omega}$ for $H^m(\Omega)$ This question focuses on the direct calculation (by change of ...
1
vote
1answer
27 views

How to show that this integral operator is bounded?

Consider the integral operator $T : C([0,1])\to C([0,1])$ given by $$Tf(t)=\int_0^1 K(t,\tau)f(\tau)d\tau.$$ I'm solving one exercise which is to show this operator is bounded. The exercise is from ...
-1
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0answers
6 views

nonlinear spreading of sound waves [on hold]

I want to get application examples, something like using spreading of sound waves in medicine branch or for musical instruments.
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0answers
35 views

Riemannian metric as an operator

In the article http://www.sciencedirect.com/science/article/pii/0370269379905896 authors consider principal bundle $P(M, G)$ and then define induced metric $g$ on $\eta = Sp(A)/G$, where $Sp(A)$ - ...
0
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0answers
29 views

Making ease-out-bounce formula have a linear start

I'm using a bounce ease out formula, the code for it: https://github.com/jesusgollonet/processing-penner-easing/blob/master/src/Bounce.java#L9. The function is copied here: ...
0
votes
0answers
7 views

$L^2$ and $C$ solutions of an initial-boundary value problem for 4$^th$ order equation

I study the initial-boundary value problem \begin{equation} \alpha^2\frac{\partial^4 w^0}{\partial x^4}+\frac{\partial^2 w^0}{\partial t^2}=P(t)\delta\left(x-\xi\right),~~ 0<x,\xi<1,~ t>0, ...
0
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0answers
6 views

Elastic Body Simple Deformation

In continuum mechanics we can consider a reference frame $B = [0,1]$ along with a homogeneous deformation $F$ where $x = Fp$ for $x \in \mathbb{R}$ and $p \in [0,1]$ and $F = 2$ so $F[B] = [0,2]$. ...
1
vote
0answers
31 views

How does the step in the picture transition to step 2?

:) I have a math question regarding this picture. The problem is that I do not understand how the first equation turns into the the second. Where did the integral come from?? (the dv and dt) Update: ...
1
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0answers
18 views

Physical Object to Pseudo-Riemannian Manifold

It is well known that Lorentzian mainfold is studied in general relativity. So this raises my curiosity about How about the classical mechanics? Does it correspond to the manifold $\mathbb{R}\times ...
2
votes
2answers
77 views

Cauchy's problem. Equation of mathematical physics

$$U_{tt} = \Delta U + x^3 - 3xy^2$$ $$U|_{t=0} = e^x \cos y$$ $$U_t|_{t=0} = e^y \sin x$$ Help me, please, with solution of this equation. Can you prompt me algorithm to find the ...
-1
votes
0answers
16 views

Hint on integrating $\int_{-L}^L \exp(-U_0 \delta(x)) dx$ [closed]

Does the following integral exist? \begin{equation} \int_{-L}^L dx \exp\left(U_0\delta(x)\right) \end{equation} And if so, what does it yield. This expression comes from a problem of a MB gas in a ...
3
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0answers
65 views

How low will a given string hang? [closed]

If I have a piece of string that is n meters long, attached at two points m meters apart, how low will the string hang? The two ...
-1
votes
0answers
16 views

AP Physics 1/2- Electrostatics Capacitor [closed]

I recently took a physics exam over Electrostatics Capacitor and was unsure about a couple of questions. the test was free response and I had to explain. Please tell me if my answer and reasoning ...
3
votes
1answer
62 views

Why are these distributions positive?

I am trying to understand some calculations in a paper by Sidney Coleman. He is showing that certain distributions are positive. The paper can be found here. What I am talking about is happening at ...
1
vote
1answer
34 views

Summation of $A\cos (\omega n+\phi)$ [closed]

I'm trying to evaluate the following summation: My original problem is $$\lim_{N \to \infty} \frac{1}{2N+1} \sum_{n=-N}^N \left|A \cos(\omega n+\phi)\right|^2$$ Now I'm stuck at calculating the ...
0
votes
0answers
34 views

Srednicki's QFT - chapter 2 - understanding from a mathematician's point of view

I am reading the first chapters of Srednicki's Quantum Field Theory book, trying to understand them from a mathematician's point of view. In particular, I'm interested to what happens when you try to ...
0
votes
0answers
12 views

wouldn' a discretized space-time violate pontryagin duality?

While this question regards physics, it is more of a mathematical question, so here it is. One often hears about attempts to model space time with tilings or some type of discretized structure. ...
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0answers
48 views

Intuitive, short explanation of differential forms and exterior calculus

Are there any introductory lecture notes on differential forms and exterior calculus, preferably aimed at physics students studying General Relativity and Black holes? I have some familiarity with GR ...
0
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0answers
9 views

Bolzmann machine cost function

Quote from Haykin book: Neural Networks and Learning Machines Third Edition From an analogy with thermodynamics, the energy of the Boltzmann machine is defined as follows: $$E(x) = -\frac {1}{2} ...
1
vote
1answer
40 views

Finding $x$ and $y$ components of Navier Stokes

An incompressible viscous fluid of constant densite and kinematic viscosity occupies the space between porous walls at $y=0$ and $y=d$. The steady two dimensional flow is subject to a constant ...
0
votes
1answer
17 views

How to calculate rotation rates of a rotating body relative to another rotating body?

I have two 3D bodies A and B, each of them is rotating around its own Z-axes with an angular velocity (e.i. yaw rate) of $\dot{\alpha}_A$ and $\dot{\alpha}_B$, respectively, relative to an absolute ...
0
votes
2answers
402 views

Centre of Mass and Moment of Inertia of a sphere - spherical cap

I have been given a sphere of radius a, from this sphere a cap of hight h is cut off. 1) What is the centre of mass of the rest of the sphere? 2) What is the moment of inertia regarding the axis of ...
1
vote
1answer
40 views

Diagonal operators on infinite dimensional Hilbert spaces

the following is a short question regarding a theorem from a quantum mechanics book I am working through but the question is a mathematical one. There is a theorem which states: Theorem: The ...
1
vote
1answer
41 views

Invere Laplace transform of a function (related to circuit analysis)

I'm studying circuit analysis. I've to solve this inverse Laplace transform to see the response: ...
0
votes
2answers
60 views

Circuit Analysis problem (find the problem)

In this question, I know that $\text{C},\text{R},\text{T},\text{A}\in\mathbb{R}^+$ I've this circuit (the bottom of the resitor is connected to earth ($0$)): When I use Laplace transform I can find ...
0
votes
0answers
30 views

Time-$t$ map of a Hamiltonian flow: how to check twist property?

I would like to obtain a general formula to verify if a certain time-$t$ map of a Hamiltonian flow is twist. I have a Hamiltonian $1$ degree of freedom system $H=H(q(t),p(t))$, such that all orbits ...
0
votes
0answers
11 views

How to model a point force with uncertain concentration point?

I consider a beam which is bent under influence of a point force concentrated at some point $\xi$ of the beam. The exact co-ordinate of $\xi$ is not known, but it is known a neighbourhood ...
0
votes
1answer
24 views

Laplace transform of a square wave function

What is the right way to find the Laplace transform of this function: The thing I noticed was: $$f(t)=\text{A}\space\space\space\space\space\space\space\space\space\space 0\le ...
0
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0answers
12 views

How to make good approximation for a sum of squared expression?

In both expression, n is integer and nmax is the maximum n and can be very large. How to use nmax to approximately and analytically to express these two expressiones? Are there any analytical ...
0
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0answers
4 views

Calculate Universal Time for when an object in orbit reaches a given radius / altitude?

Assuming that an object in orbit WILL reach a given radius / altitude at some point in the future, how can I work out the exact time it will reach that point? Assume that the object is a Satellite in ...
2
votes
1answer
42 views

Ellipsoid moment of inertia matrix

Some background info: torque $\tau$ is defined as $$\tau = I*d\omega$$ Where $I$ is the moment of inertia matrix and $d\omega$ is an object's rotational acceleration. As I understand it, the inertia ...
58
votes
7answers
5k views

What is “Bra” and “Ket” notation and how does it relate to Hilbert spaces?

This is my first semester of quantum mechanics and higher mathematics and I am completely lost. I have tried to find help at my university, browsed similar questions on this site, looked at my ...
2
votes
1answer
28 views

Unique ground state of Schrödinger Operators

I'm reading a book and there is an argument that the ground state of a Schrödinger operator is unique. The problem is I think the argument is complete non-sense! These are lecture notes by Witten, I ...
0
votes
0answers
24 views

prove de Rham cohomology of S,the “spherical universe,” is 0-dimensional?

How to prove de Rham cohomology of S,the "spherical universe," is 0-dimensional?(Here, S is a rectangle where if you exit the right, the enter from the top and if you exit the left, the enter from the ...
-1
votes
1answer
79 views

Employing Newton's Laws with differential equations [closed]

Going through some problem sheets from previous semesters and can't find a full solution for this question so was wondering what the answers might be. A particle of mass $m$ moves on the $x$ axis ...
1
vote
1answer
83 views

Figuring out velocity,acceleration, work of a particle given that we know its position vector.

Recently this question came up in a problem class of mine. A particle moves in such a way that its position vector at any time $t$ is $\vec{r}(t)=\pmatrix{A\sin{\omega t}\\A\cos{\omega t}\\Bt^2}$, ...
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0answers
30 views

Seperation of variable Heat equation

Consider a copper bar of length $L = 100cm$ which is kept at the temperature $u = 0\space °C$ at one end, and is perfectly insulated at the other end. The bar is initially heated according to the ...
0
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0answers
11 views

Regularity of Fourier transform?

Let $ |k|^n\cdot\,\hat{u}(k) \in L^2(\mathbb {R} ^d)$. Can we make a statement about the regularity of the $u$ itself? The idea would be to use the differentiation rules for the Fourier transform, ...
3
votes
0answers
28 views

Dissipation term in wave equation

If we're given a string with mass density $\rho$ in units $\frac{M}{L^3}$ with constant cross-section $A$, tension $T$ in units $\frac{F}{L^2}$, and whose length is $L$; and then we assume that the ...
0
votes
1answer
28 views

Calculate position with increasing acceleration.

So if calculating the change in an object's position (with a constant acceleration) is done with this equation: $o = vt + (\frac12)a t^2$ $o$ is offset from original position $v$ is starting ...
1
vote
1answer
38 views

Mcgehee transformation, conversion to polar coordinates and blowing up the singularity

I am looking for any reference on the above topics as I am struggling to convert the below to polar coordinates in phase space: The system is: \begin{equation*} x''=\frac{-\mu x}{(\mu x^2 + ...
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0answers
21 views

Writing PDE in the form of convervation law

What does one need to know in order to write $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+\frac{\partial^3 u}{\partial x^3}=0$ in the form of a conservation law, which contains the ...
2
votes
1answer
21 views

Computate the commutator $[p^n,x]=-ihnp^{n-1}$

Computate the commutator of $[p^n,x]=-ihnp^{n-1}$. With $p=-ih \frac{\delta}{\delta x}$ the impulse operator. $h$ stands for $\frac{h}{2\pi}$. Answer: I do it with induction over $n$. For $n=1$ ...
0
votes
1answer
17 views

What's the value of $\int f(x)\delta(x-a) dx$ if $a$ is not in the domain of integration?

A problem occurs when I was solving an exersice of perturbative kind. The delta function has the fundamental property that \begin{align} \int_{-\infty}^{\infty}f(x)\delta(x-a)dx=f(a) \end{align} ...