# 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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### 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 ...
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### 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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### 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 ...
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### 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 ...
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### 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 ...
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I'm studying circuit analysis. I've to solve this inverse Laplace transform to see the response: $$\mathcal{L}_{s}^{-1}\left[\frac{r}{r+\frac{1}{cs}}\cdot\frac{k\tanh\left(\frac{as}{2}\right)}{s}\... 0answers 14 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 ... 1answer 30 views ### Unique ground state of Schrödinger Operators I'm reading a book and there is an argument that the ground state of a SchrÃ¶dinger operator is unique. The problem is I think the argument is complete non-sense! These are lecture notes by Witten, I ... 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 ... 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 ... 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, ... 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 ... 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 Â°C at one end, and is perfectly insulated at the other end. The bar is initially heated according to the ... 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 ... 1answer 45 views ### Ellipsoid moment of inertia matrix Some background info: torque \tau is defined as$$\tau = I*d\omegaWhere I is the moment of inertia matrix and d\omega is an object's rotational acceleration. As I understand it, the inertia ... 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 ... 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 ... 1answer 22 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 it ... 1answer 84 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}, ... 1answer 40 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 + y^2)^{... 1answer 18 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} ... 0answers 85 views ### A version of Ampère's law The most common proof that I have found of the fact that AmpÃ¨re's law is entailed by the Biot-Savart law uses the fact that, if \boldsymbol{J}:\mathbb{R}^3\to\mathbb{R}^3, \boldsymbol{J}\in C_c^2(\... 2answers 33 views ### Integral path between 2 points so I need your help calculating the next inegral: Calculate the integral\int(10x^4-2xy^3)dx -3x^2y^2dy$$at the path$$x^4-6xy^3=4y^2$$between the points O(0,0) to A(2,1) please explain me ... 0answers 12 views ### how to integrate a equation in Ito formulation Does any one know how to integrate the differential equation in Ito formulation. I have following stochastic equation in Ito form:$$dx=x(1-x)dW(t)$$where dW(t) is the Weiner increament such that \... 1answer 36 views ### need help for integrating the differential equation I am not able to integrate the following stochastic equation. The equation is$$\frac{dx}{dt}=g(1-x^2)x+\sqrt{g}(1-x^2)\xi(t)$$g is a constant and x is defined between -1 and +1. \xi(t) is ... 1answer 18 views ### Symmetry of Green's function on the general case Let's consider the differential equation$$\nabla\cdot[p(\mathbf{r})\nabla u(\mathbf{r})]-s(\mathbf{r})u(\mathbf{r})=-f(\mathbf{r}).$$I want to show that the Green's function is symmetric, so that ... 0answers 51 views ### How to construct a G-extension of a category C? Note: I'm a physicist so this will be phrased somewhat in physics language. Suppose we have a unitary modular tensor category \mathcal{C}. In physics language, we can think of \mathcal{C} as ... 0answers 25 views ### how do I resolve equations that are both dependant on each other I'm working on a project concerning the ideal power equation of aerodynamic bodies seen here:$$P = \frac{1}{2}C A D v^3 + \frac{W^2}{Db^2v}$$where P = power, C = coefficient of drag, A = ... 1answer 63 views ### Helmholtz decomposition of a vector field on surface Does it make sense to do Helmholtz decomposition of a vector field defined on a surface or on a manifold? I am mostly interested in the surface case. I was trying to find a reference for this and ... 1answer 26 views ### Uniqueness for Dirichlet problem in exterior domain I have the following problem: \Delta u =0 in \Omega_e = \mathbb{R}^3 - \overline{\Omega}, and with condiction u=0 on \partial \Omega and u=o(1), that is \lim_{r \rightarrow 0} u(x) =0. ... 0answers 22 views ### Converse of this theorem about existence of Green's function I've been solving some problem which asks us to find the Green's functions for some problems when it exists. Now, there's a theorem which allows us to guarantee that it exists. The theorem is as ... 1answer 52 views ### Interpretation of Equations of Motions I started a lecture on differential equation with following example. If a body is moving in a straight line in plane with constant speed, how can we describe this motion mathematically? To answer ... 0answers 63 views ### Cubes in cubes in cubes in… ad infinitum. Suppose I have a cube with one open side (with a volume of let's say 1\ m^3) for the sake of simplicity; the problem is scale invariant) made from a material that makes the cube just float in water ... 0answers 31 views ### Heat problem with an internal source of heat for which the maximum principle doesn't hold. Heat problem with an internal source of heat for which the maximum principle doesn't hold. The problem is the following and honestly I don't know how to solve it...$$u_{t}=u_{tt}+2(t+1)+x(1-x) , 0&...
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given a projectory equation of the form $y=y(x)$find the curvature radius as a function of $x.$ a projectory equation , hence $x=x(t)$, input that in y and we get $y=y(x(t))$, which is what one ...
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### The Virasoro-Bott group and the KdV equations

The Euler Arnold equation expresses equations (usually from mathematical physics) as geodesic equations on a Lie group. For the famous $KdV$ equations these equations are given on the Virasoro-Bott ...
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