"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
2answers
29 views

Multiplying two Scalar dot products together

stackexchange community, I'm just wondering what the rules are for multiplying dot products together, such as: $$ (P_{3}\cdot{P_{4}})(P_{1}\cdot{P_{2}}) $$ How would this be expanded out to not ...
-1
votes
0answers
24 views

volume of the air bubble in the water [migrated]

How does the depth affect the volume (the radius) of an air bubble in the water, if the temperature and density of the water are constant. Is there any relation combining this?
0
votes
0answers
12 views

virtual work and potential energy

I was just going through the thermal and elastic buckling of bars & plates ,I found some researchers use virtual work to derive the equations, another researchers use potential energy in other ...
0
votes
2answers
27 views

Anyone know how I would linearize this data

I think it might be a cubic function,however I am unsure of how I would linearize the data in order to find the regression equation. hi ian.
0
votes
0answers
31 views

how to linearize a cubic function [on hold]

So I have been trying to linearize this data for almost a month now, teacher and I have no clue what to do. Help would be greatly appreciated
4
votes
7answers
384 views

Books for studying Mathematical Physics?

Currently I'm doing Advanced Classicial Mechanics courses.I'm finding it hard to understand due to the lack of knowledge in linear algebra, multi variable calculus and other chapters. Can anyone ...
1
vote
1answer
50 views

Compare analytic model with numerical, mass spring system.

So I'm trying to solve a problem here and I have been working on it all day, clearly i'm in need of some guidance. I have a rod of length $L$ and cross section area $A$, Young's modulus $E$ and ...
1
vote
1answer
19 views

Solving Laguerre coefficients with Integral?

I'm having some difficulty understanding the solution to a particular Laguerre expansion. The problem reads "Expand the term $ e^{-x}$ as a Laguerre expansion, noting the orthogonality of $$ < ...
0
votes
0answers
36 views

Having trouble interpreting the geometry of this setup.

A circular conductor, with cross section given by $(x-d)^2+y^2=b^2$, i.e. radius $b$ and centered on $x=d$, has a circular core, made up of the interior of the circle $x^2+y^2=a^2$, with ...
18
votes
7answers
3k views

Mathematics needed in the study of Quantum Physics

As a 12th grade student , I'm currently acquainted with single variable calculus, algebra, and geometry, obviously on a high school level. I tried taking a Quantum Physics course on coursera.com, but ...
0
votes
1answer
33 views

Why the equivariant volume of a non-compact space can be finite?

I am very confused with equivariance (equivariant cohomology etc). In specific when one tries to evaluate the equivariant volume of, say, $\mathbb{R}^2$ (with coordinates $x,y$) one finds that it is ...
7
votes
6answers
423 views

Proving that $E=mc^2$ [closed]

What are the axioms of special relativity? Is there a book or paper that introduces the theory of special relativity in a rigorous manner, and proves that $E=mc^2$ after appropriate definitions?
1
vote
0answers
40 views

Acceleration of an air bubble under the sea

An air bubble arises from the bottom of the sea. Find its acceleration if the resistance force is proportional to $\rho$*A*$v$ where $\rho$ is density of water, A is cross section area and $v$ is ...
0
votes
1answer
65 views

How to express this equation in terms of v?

I read from my physics textbook that the magnitude of a ripple voltage decreases if the capacitance is increased in a rectifier circuit, but the textbook didn't specify what the exact mathematical ...
0
votes
1answer
31 views

First Order Differential Equation for a Harmonic Oscillator

A box with mass $m$ is attached to a spring with spring coefficient $k$. This system is then placed into a glass case filled with a liquid with drag coefficient $\alpha$. Now I have the following ...
2
votes
0answers
35 views

Coset Space as a Representation of a Lie Algebra

I'm reading through some notes (about the use of Lie groups/algebras in physics) obtained from a friend from a class that took a while back, and I can't quite figure out where one thing regarding some ...
0
votes
1answer
33 views

More equations than unknowns for maxwell equations?

I had one curiosity regarding maxwell equations in 3-D From the curl equations, you get 6 unknowns, with 6 equations. The divergence equations add 2 additional equations. When these are combined, we ...
2
votes
1answer
53 views

How do I determine if the equation is a conservation law?

We have the PDE $\frac{\partial u}{\partial t}+a(x,y)\frac{\partial u}{\partial x}+b(x,y)\frac{\partial u}{\partial y}=0$. What would be conditions on $a$ and $b$ for the equation to constitute a ...
12
votes
1answer
157 views

Interpretation of an integral transform from the wave equation to the heat equation

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}\ ...
0
votes
0answers
28 views

How can we prove that the derivative of a generalized Hilbert space valued Brownian motion is a Gaussian white noise?

Let $(\Omega,\mathcal A,\operatorname P)$ be a probability space $\lambda$ be the Lebesgue measure on $[0,\infty)$ $\mathcal D:=C_c^\infty([0,\infty))$ and $\mathcal D'$ be the dual space of ...
5
votes
1answer
102 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: ...
4
votes
0answers
42 views

Physical meaning of Hawking's Singularity theorem

I'm studying O'Neill's "Semi-Riemannian Geometry with applications to Relativity". I know that the following theorems are related to the Big Bang, but I don't understand how. Let $M$ be a ...
0
votes
1answer
22 views

Frobenius method to solve differential equations, different \alpha found

I am referring to Carl Bender's Advanced mathematics methods for scientists and Engineers. Well, actually I know how to solve it....However, if I choose to do a so called "powerful" method,which is ...
1
vote
3answers
26 views

Where does the extra $\omega$ come in velocity of Simple Harmonic Motion?

Position $x$ in a SHM is given by $x=A\space sin(\omega t+\phi)$. Where $A$,$\omega$ and $\phi$ are Amplitude,Angular frequency and phase constant and are three constants respectively. So,velocity ...
1
vote
1answer
14 views

Odd Vector Product Question

Here is a question that has me stumped: Use the geometric definition to find: $2 {\bf i} × ({\bf i}+{\bf j})$ Student solution manual says: By the definition of cross product, $2 {\bf i} × ({\bf ...
0
votes
0answers
34 views

Is this partial differential equation solvable?

Ok so I am asked to set up a partial differential equation and then motivate why it is solvable. I'm only 2 weeks into my course so we are not asked to solve anything yet. However, if someone would ...
0
votes
1answer
30 views

find angle given point the trajcetory passes through and inital velocity

I'm currently studying M1 for A level maths and we've derived the equation to prove that the trajectory is a parabola. $y=x\tan\theta - \sec^2\theta \dfrac{gx^2}{2u^2}$ I am curious as to how to ...
0
votes
0answers
16 views

Trajectory of an object under gravity

Is there an equation (cartesian/polar)depicting the trajectory of the motion of an object relative to another (in a two body system) under gravity?
1
vote
1answer
49 views

Solving differential equation describing motion in a pendulum

I've been looking at Simple Harmonic Motion in particularly the period of a pendulum. This may seem like physics but my question is tailored towards mathematics. The differential equation is: ...
0
votes
0answers
26 views

Alternative expression of a Gaussian integral over complex variables

We construct an $N\times N$ matrix $J$ whose elements are drawn from Gaussian distribution with zero mean and variance $\frac{1}{N}$. Since we want to have different variances for different columns, ...
0
votes
0answers
19 views

Runge-Kutta 4 in polar coordinates

How is the Runge-Kutta method implemented on this differential equation: $$ \frac{d^2 \theta}{dt} = -\frac{g}{l} \theta $$ (pendulum motion) which is in polar coordinates? Let: $c = \frac{g}{l}$ ...
1
vote
1answer
25 views

Velocity Verlet method: How to calculate acceleration

The velocity Verlet method algorithm is as follows: Calculate: $$\vec{x}(t + \Delta t) = \vec{x}(t) + \vec{v}(t)\, \Delta t+\tfrac12 \,\vec{a}(t)\,\Delta t^2$$ Derive: $\vec{a}(t + \Delta t)$ from ...
0
votes
0answers
35 views

Definition of Global Information and Local Information (CS)

I am a research student of computer science, I always feel like there are some thing missed when I am trying to define some concept mathematically. For example, I would like to define two concepts: ...
0
votes
0answers
70 views

Integration of the product of Hermite Polynomial and exponential function

how to proceed with these two integration.. $$\int^0_{−∞}e^{−ax2}H_{2k}(x)dx=?$$ $$\int^∞_{0}e^{−ax2}H_{2k}(x)dx=?$$ where $$H_n(x)$$ is the Hermite Polynomial (physicist's convention).
0
votes
0answers
11 views

Hamiltonian Elliptical Path

For a Hamiltonian of the form, $$ H = \frac{1}{2} p_i p^i - \frac{k}{\sqrt{q_iq^i}} $$ which is a Hamiltonian for a gravity system or something similar. These systems are know to have paths that ...
4
votes
0answers
60 views

Backgrounds of the p-Laplacian Operator

Motivation I encountered the following partial differential equation (PDE) in a mathematical paper $$\begin{array}{} u_{tt}+\Delta^2u-\nabla\cdot\left(|\nabla u|^{p-2}\nabla u\right)-\Delta ...
0
votes
0answers
33 views

A computation from an article in computational neurosciences (from physical review) which doesn't fit

I am reading this article (with this erratum) in computational neuroscience, and there is a computation there that simply doesn't fit.. Maybe one of you can see something that I am missing? For the ...
0
votes
0answers
25 views

Semi-infinite forms?

I am reading Vafa's paper 'Topological Mirros and Quantum Strings'(arXiv:hep-th/9111017). In this paper, the author says the Hilbert Space of a fermionic string theory corresponds to the space of ...
1
vote
0answers
22 views

Cyclic permutation

How did the author do the cyclic permutation? $\Gamma^k_{ij}g_{kl}+\Gamma^k_{lj}g_{ki}=\partial_jg_{il}$ We can cyclically permute these indices to generate two more equations: ...
2
votes
1answer
27 views

How can I prove that for a Killing vector $\nabla^a \nabla_a \xi^\mu = -R^b_a \xi^a$?

I'm taking a course on General Relativity and I'm trying to prove that for a Killing vector field $\xi^\mu$ the following equation holds: $$\nabla^a \nabla_a \xi^\mu = -R^\mu_a \xi^a$$ Where ...
5
votes
1answer
559 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: ...
3
votes
2answers
46 views

Calculating segment length on circle

I'm building a physical machine and I'm trying to figure out a geometrical problem. The machine is composed by a cylinder, and the wall of this cylinder is composed by many wooden boards, each of ...
1
vote
0answers
18 views

Simple Harmonic Motion; Tension in Elastic rope

I'm struggling to model this question out correctly. A glider and its pilot have total mass $230$ kg. The glider lands on a horizontal airstrip and when its speed is $16$ m/s it hooks on to the ...
1
vote
1answer
35 views

Page 72 of Courant and Hilbert's Methods of Mathematical Physics, Vol 1.

We have the following identities: $$ \beta_\nu = b_\nu -\frac{1}{2}(b_{\nu-1}+b_{\nu+1}),\ \ \ \ (\nu=2,3,4,\ldots)\\ \beta_1=b_1-1/2 b_2 $$ $$s_n(x)=\sum_{\nu=1}^n b_\nu \sin(\nu x) \\ ...
3
votes
1answer
59 views

Momentum is quantised in compact spaces?

Background One of the first examples given when studying quantum mechanics is the particle on a cylinder, or particle on a ring. One finds that because of the periodic boundary conditions, ...
0
votes
1answer
27 views

A proof in Hilbert & Courant vol 1 of Weierstrass theorem.

My question is regarding a derivation of an inequality on page 67 of Methods of Mathematical Physics. Here's a scan of the book: ...
1
vote
1answer
415 views

How to convert FFT magnitude of square wave to dBm?

I wish to convert the FFT magnitude of square wave into dBm. I use FFT to covert voltage of square wave to a complex number, then i absolute the complex number into magnitude. Then i divide the ...
0
votes
1answer
15 views

Dividing before and after integration give different results

I'm having a physics exercise, but the question is more of math. Assuming I have the following constants: $m_1, m_2, \alpha, V_0$ and two variables: $v, t$. (v as velocity). I reach the following ...
0
votes
1answer
18 views

Difference between 'principal of indifference' vs 'the assumption of equal a priori probabilities'?

Is there a difference between the "principal of indifference" and "the assumption of priori probabilities" and if so what? If there is no difference why the use of two different terms? EDIT I have ...
1
vote
1answer
39 views

(Distributional) Fourier transform

I need to calculate the (distributional) Fourier transform of $$ f(x) = \frac{x^2}{x^2+1}. $$ I unsuccessfully tried to find a differential equation for $f$ in order to solve the Fourier-transformed ...