"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 ...

learn more… | top users | synonyms (1)

0
votes
1answer
47 views

Show that requiring Electrostatic potential to be a stationary point of Electrostatic potential energy is equivalent to Laplace's equation.

Suppose we want to find the electrostatic potential $\phi$(r) inside of some volume $V$ with known boundary conditions. The physical field configuration should minimize the electrostatic potential ...
1
vote
0answers
51 views

Diagonalization of total angular momentum over creation operators for an isotropic harmonic oscillator?

You have an isotropic three dimensional quantum harmonic oscillator so the Hamiltonian is $$ H=\frac{p^2}{2}+\frac{r^2}2 $$ If you do the creation-annihilation operator-algebra trick and define ...
1
vote
1answer
74 views

Lagrangian equivalence up to total time derivative: dependence on higher derivatives

I recently encountered the problem Show that the Euler-Lagrange equations of motion for $L_1$ and $L_2$ are the same when $$L_2(\ddot{q},\dot{q},q,t) = L_1(\dot{q},q,t) + \frac{d}{dt} ...
0
votes
0answers
26 views

What are the non-linear representations of $SO(3,1)$?

The classification of the representations of the Lorentz group $SO(3,1)$ is well known, but the representations are usually expressed in linear form. My question is whether there is a framework to ...
1
vote
1answer
30 views

Books for Tensor Algebra used in Physics?

I'm taking a dual Math,Physics undergraduate course.I want to study GR and a few parts of relativistic Quantum Mechanics.I've a decent amount of knowledge in linear algebra. Though we have tensor ...
0
votes
0answers
15 views

Heinrich Hertz on Mathematical Equations

What is the quote from Heinrich Hertz on how he could never exhaust the meaning behind a mathematical equation? (It's not mentioned in the Hertz quotations here.)
2
votes
1answer
34 views

Does Lagrangian always exist for any equation?

In mathematical physics, a lot of equations can be interpreted as a solution of least action principle for some Lagrangian. I wonder if for every equation there is a Lagrangian so that one achieves ...
0
votes
1answer
21 views

one-dimension motion

A rock is thrown vertically up at 80 ft/s. Find it's maximum height, time of flight, and final velocity as it passes the starting point. So for my parameters I have: initial y=0 final y=? ...
1
vote
1answer
31 views

Prove $ \nabla \cdot (f \nabla \psi ) = \nabla f \cdot \nabla \psi + f \nabla ^2 \psi $ in general curvilinear coordinates.

Prove $ \nabla \cdot (f \nabla \psi ) = \nabla f \cdot \nabla \psi + f \nabla ^2 \psi $ in general curvilinear coordinates. I have been attempting to do this using general curvilinear dot products ...
3
votes
1answer
110 views

How to publish a mathematics/physics book?

I have recently finished a mathematics/physics book (the title is "N-DIMENSIONAL TIME & 1-TIME DIMENSIONED HISTORIES"). The printed version is ~100 pages long. I have worked all my life as an ...
0
votes
1answer
44 views

Visual understanding of convergence of domains in the sense of Fisher

In these lecture notes by Ueltschi here, I found in Definition 2.3 a peculiar type of convergence. Especially the second property is hard for me to visualize what it means, could anybody try to ...
1
vote
1answer
19 views

Find the average acceleration

Find the average acceleration of the tip of the 2.4-cm long hour hand in the interval noon to 6pm. I found the average velocity is -2.2x10^6 but I'm not sure how to go about finding acceleration. If ...
0
votes
1answer
33 views

help setting up a velocity question

Standing on the ground from 3.0 m from a building, you want to throw a package from your 1.5- shoulder level to someone in a window 4.2 m above the ground. At what speed and angle should you throw ...
0
votes
0answers
57 views

Relative motion question

You wish to row straight across a 63-m-wide river. You can row at a steady 1.3 m/s relative to the water, and the river flows at 0.57 m/s. I know I need to draw a right triangle for the question but ...
-1
votes
2answers
24 views

For the following voltage waveform, determine the frequency f, peak voltage amplitude Vp and phase [closed]

For the following voltage waveform, determine the frequency f, peak voltage amplitude Vp and phase $ v(t)=6sin(2\pi 10000 t+30^0) Volts $ the solution is f=10KHZ Vp=6 volts $ phase =30^0 or, \pi/6 ...
1
vote
1answer
37 views

List of well-known submodular function in physics, statistics, math?

Can you please share a list of well-known submodular functions (have the diminishing return property) that you know? In physics, stats, math, etc? I am searching for a submodular function for my ...
1
vote
1answer
195 views

Work on Springs using Hooke's Law

I'm currently stuck on parts c and d of this problem. The problem says Suppose a force of 20 N is required to stretch and hold a spring 0.4 m from its equilibrium position (0). I found k constant to ...
2
votes
0answers
33 views

Liouville's theorem (Hamiltonian) [closed]

can some one give me a link for a rigorous proof for Liouville's theorem (Hamiltonian) thanks
0
votes
1answer
40 views

Irrationality of $\alpha$ the fine-structure constant. [closed]

Is the fine-structure constant rational, or irrational? I have asked this question on the physics stack exchange, but I want to get some mathematicians' perspectives as well.
0
votes
1answer
30 views

Solving Coulomb Integral in 1D

I am trying to solve the following Coulomb integral of two gaussians: $$ \int_{- \infty}^{ \infty}dx1\int_{- \infty}^{ \infty} \frac{e^{-b1 (x1-c1)^2}e^{-b2 (x2-c2)^2}}{\left | x1-x2 \right |}dx2, $$ ...
0
votes
2answers
27 views

How to calculate the direction (of velocity of a ball) after collision with another ball?

Say I have two balls of same radius, in the 2-D Plane. So like a pool (billiard) game. I have the cue ball, moving with the velocity vector V, the magnitude is not important, so we only need an angle ...
1
vote
1answer
62 views

derivative chain rule in a triangle, confusing but interesting problem

Refer to the above figure. Assuming the length of the 3 edges of triangle are $r_0,z_0,\xi_0$. And we have $\xi=\sqrt{r^2+z^2}$ (Eqn.1)and $\xi_0=\sqrt{r_0^2+z_0^2}$. The normal vector on the ...
0
votes
1answer
35 views

Prove scalar product is distributive

The scalar product is defined as r*s = the sum of all r*s. Using this definition, prove that r*(u+v) = r*u + r*v. Also, if r and s are vectors that depend on time, prove that the product rule for ...
1
vote
2answers
54 views

Deriving the kinematic equation $v^2=v_{0}^2+2a(x-x_{0})$.

I have a question on deriving the kinematic equation $v^2=v_{0}^2+2a(x-x_{0})$ from first principles and the known kinematic equations. Is this simply differentiating, but with respect to time($t$)? ...
1
vote
1answer
45 views

Minkowski space is locally Euclidean?

The Minkowski spacetime $\mathbb{R}^{1,3}$ is said to be a manifold (isomorphic to $SO^{1,3}$. But according to the definition of a manifold it should be locally euclidean. However, this seems to be ...
0
votes
0answers
16 views

Description of distributions with support in a linear subspace

The following lemma is true: any distribution $\lambda$ on the real line with support included in $\{0\}$ can be written as $$ \lambda = \sum_{i = 0}^N a_i \partial^i(\delta_0)$$ with the $a_i$ being ...
1
vote
1answer
58 views

Longitude and latitude problem

I find this question challenging. I am trying to solve this question for my younger brother. So here it goes: An airplane leaves an airport $X$, 20.6$^0E$ and 36.8$^0N$, and flies due south along the ...
1
vote
0answers
42 views

Is Hodge star operation can be understood as contraction after tensor product of a $p$-form with the volume element?

By defintion, the Hodge star of a $p$-form $\omega_{a_1\cdots a_p}$ on a $n$-dimensional manifold is given by $*\omega_{b_1\cdots b_{n-p}}=\frac{1}{p!}\omega^{a_1\cdots a_p}\epsilon_{a_1\cdots ...
3
votes
1answer
50 views

Complex charge in RLC circuit

Calculate the absolute value of the complex charge in the RLC circuit: $$Q(t)=\frac{V_0e^{i\omega t}}{-\omega^2L+i\omega R+\frac{1}{c}}.$$ Find the frequency where $|Q(t)|$ is maximum. This ...
0
votes
2answers
66 views

How to find a vector normal to a cylinder in cylindric coordinates?

I'm trying to solve a problem which demands to multiply a vector M and vector normal to a cylinder's surface in cylindric coordinates. Height of the cylinder is infinite and its radius is R. So how do ...
0
votes
2answers
24 views

Finding vertical displacement

I am being asked to find the distance a shuttle travels upward after a given amount of time. I know that time passed is 79s, the rate of acceleration is 6.244 m/s^2, and the speed at 79s is 493.276 ...
3
votes
1answer
59 views

How to mathematically determine if the magnitude of a cross product is up/down(positive/negative?)?

So, I'm a newbie at complex vector math. I'm working on a 2D physics engine, and my issue is, with angular acceleration from torque, is it supposed to be positive or negative? I understand the right ...
0
votes
2answers
35 views

Vectors, How to measure total force and direction.

I am currently looking for some math help that I am quite struggling with. The problem is: (Vectors) A fisherman use his pole and line to pull a fish out of the water. The line exerts a force on ...
1
vote
1answer
83 views

Is 1/x the “slowest” asymptotically falling off differentiable function?

As a physicist, I tend to think about $\sim 1/x$ as the "slowest" fall-off of a "reasonable" function. Let us state this formally: $${\rm lim}_{x \to \infty} f(x) = 0, f(x) \in Reas \implies \exists A ...
1
vote
2answers
78 views

Water Refraction and the depth of the water.

I'm not sure if this is the right place to ask my question! But I hope I will find some help!. Image distortion occurs by refraction of light at the boundary surface between air and water when a ...
2
votes
1answer
56 views

Why does a heating model work?

I am referring to: $T=T_0 e^{kt}$ where T=temperature,t=time and k=constant. It seems to work, I as just curios to why it works?
1
vote
1answer
76 views

Losing all races by the same margin of time

Suppose two cars are racing along a (straight) road at a constant speed $v_{0}$ m/s. At time $t = 0$, Car 2 is ahead of Car 1 by $d_{0}$ meters; or, one could say, Car 1 is losing by $d_{0} / v_{0}$ ...
1
vote
0answers
36 views

Formally evaluating integral to calculate electric or gravitational field.

I never understood how such integrals are calculated, formally. In a line is easy, just a line integral. In a surface, sometimes is easy, like in a disc. But, some surfaces, like sphere, it gets ...
2
votes
0answers
37 views

Resolvent and spectrum of a self-adjoint extension

In this paper, they give the resolvent, spectrum, and eigenfunctions of the self-adjoint extension of the Laplacian on a rectangle that corresponds to a delta potential at an arbitrary point (items ...
2
votes
2answers
43 views

Calculate initial speed to launch the cat at specific spot

BACKGROUND: I’m trying to create a game where cat jumps from platform to platform, but as any other cat this furry devil won’t do the things I’m asking for. I want the cat to jump and land at the ...
0
votes
2answers
65 views

Solving a differential equation numerically to plot particle path

I'm trying to plot the evolution of a particle in an accretion disk by solving the equation $$2X\frac{\partial X}{\partial\tau}=V_R(X,\tau)$$ where I have found $V_R$ numerically to be ...
1
vote
1answer
53 views

Angular momentum of an accretion disk

I need to plot the time evolution of the total angular momentum in an accretion disk. This confuses me because I thought this should be constant, since angular momentum has to be conserved? I'm given ...
6
votes
0answers
146 views

Making new sense of the three-body problem in the light of Maryam Mirzakhani math contributions

I am unfamiliar with moduli spaces and ergodic theory which appear to be essential in Maryam Mirzakhani's math contributions which won her the Fields Medal. However, I am well conversant with ...
0
votes
0answers
24 views

Examples of quasilinear wave equations

Consider a quasilinear wave equation equation of the form $\sum g^{ij}(u, Du)\partial_i\partial_j u = F(u, Du)$ on $R \times R^n$ subject to initial data $u(0,x)=g, \; \partial_t u(0,x)=h.$ Given ...
5
votes
0answers
137 views

Learning roadmap to Topological Quantum Field Theories from a mathematics perspective

I want to learn TQFT's and am looking for review articles or books. My mathematics knowledge is limited to one year of graduate course in Algebra (Groups,Rings,Fields,Categories, Modules and ...
0
votes
0answers
22 views

Conformal transformation

The problem is following. This is an Exerciese of Polchinski $2.6$ (explanation about conformal field transformation) Consider the flat Euclidean metric $\delta_{ab}$ in $d$ dimensions. An ...
1
vote
0answers
38 views

Lecture notes on holomorphic Yang-Mills theory

Some time ago I've found these lecture notes on the gauge theory. In particular, in these lecture notes the author introduces and studies the Yang-Mills equations in the case of real bundles and ...
1
vote
1answer
63 views

Simple Harmonic Motion DE

The simple harmonic motion DE is $x''(t)=-x(t)$ I solved it as a homogenous linear equation and after inserting the Euler's formula into the equation, my solution becomes ...
0
votes
1answer
97 views

Trigonometry in projectile motion

I initially posted this question on Physics SE but got no responses probably because it's more related to maths than physics. A plane surface makes an angle $\bf X$ with the horizontal. From the ...
3
votes
0answers
64 views

My orbiting body is orbiting about the wrong focus of it's elliptical orbit… why? [closed]

I am coding in c++ and am computing the position of an orbiting body as a function of time. Everything is almost working. I have a nice elliptical orbit. Except, my orbiting body speeds up as it ...