"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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Wave front set of a corner

Consider the distribution $u$ defined on $\mathbb{R}^2$ by $$ u(x, y) = \begin{cases} 1 &\text{if } 0 < x < 1;\, 0 < y < 1, \\ 0 &\text{otherwise}.\end{cases} $$ What is the ...
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29 views

Calculating where a snowball lands if it doesn't hit anything while falling?

In my calc based physics class we were given the following question, which I've had a lot of trouble with: A snowball rolls off a barn roof that slopes downward at an angle of $40^∘$. The edge of the ...
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64 views

Geometric Quantization

I'm curious about geometric quantization. Of course, I know the procedure: Start with a classical phase space $T^{*}X$, $X$ is the configuration space, then do prequantization by creating a ...
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32 views

Quantization and evaluating a complex function on multiple Riemann sheets

In Lecture 3 of his mathematical physics course, Carl Bender mentions that the evaluation of a complex function on multiple Riemann sheets can be used to describe the quantization of the laws of ...
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56 views

Axiom of choice in proof of Wigner's theorem?

In Appendix A of chapter 2 of "The Quantum Theory of Fields," vol. 1, Weinberg presents a proof of Wigner's theorem: given a symmetry transformation $T$ of rays, one can extend this to a symmetry ...
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46 views

How to show that Yang-Baxter equation is the same as braid equation?

The quantum Yang-Baxter equation is $R_{12}R_{13}R_{23} = R_{23}R_{13}R_{12}$. The braid equation is $R_{12}R_{23}R_{12}=R_{23}R_{12}R_{23}$. It is said that these two equations are equivalent. How to ...
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29 views

Don't understand how this answer is arrived at; dynamic power

According to my notes the fomula for dynmaic energy is $\frac{1}{2}capacitive load \times voltage^2$ and formula for dynamic power is $\frac{1}{2}capaxitive load \times voltage^2 \times switching ...
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47 views

Help with solving a problem involving motion in 2D [closed]

A physics book slides off a horizontal table top with a speed of $1.55\:\text{m s}^{-1}$. It strikes the floor after a time of $0.430\:\text{s}$. Ignore air resistance. Find the height of the ...
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48 views

Strong versus weak coupling expansion to solve hard problems

For the quintic equation $$ x^5 + x = 1 $$ it can be seen that when taking the strong coupling limit to solve $$ x^5 + \epsilon x = 1 $$ perturbatively, summing the terms of all orders in ...
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89 views

Conformal Mapping preserves the angles between the smooth curves.

I am interested to proof that conformal mapping preserves the angles between the smooth curves. I will be greatful if anyone can help me in it.
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44 views

Finding Orbital Period of an Object

A satellite is launched to orbit the Earth at an altitude of $1.55\times10^7$ m for use in the Global Positioning System (GPS). Take the mass of the Earth to be $5.97\times10^{24}$ kg and its radius ...
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187 views

Finding Acceleration of Two Objects Touching

Alex is asked to move two boxes of books in contact with each other and resting on a rough floor. He decides to move them at the same time by pushing on box A with a horizontal pushing force FP = 8.7 ...
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39 views

Minimizing a functional by variation

I have a problem at the last step of my proof. I have the following functional to be minimized on $\rho\in L^1(\mathbb R^d)$. Here $\lambda$ is a Lagrange multiplier and $\rho\geq 0$. $h(\rho) = ...
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23 views

Looking for a translation

Reading the book "Fundamentals of Renewable Energy Processes I came across an equation I am not sure how to read. The equation is: $$J_0=q\frac{4\pi}{h^3}mk^2T^2exp(-\frac{q\phi}{kT}) $$ I am looking ...
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148 views

Are continuous mathematical models of discrete physical phenomena messy because of a disconnect between “continuous” and “discontinuous”?

Examples from statistical mechanics and continuum mechanics abound: a discrete phenomenon (e.g. kinetic energy of molecules) is "averaged" out over the constituents of the system to which it applied ...
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21 views

Getting the Amps from Watts, Amps and the voltage of a line

What amperage capacity should the supplied wired be rated for a refrigerated fixture which has a 208V power supply and the following loads? 4 Evaporator fan motor rated at 9W each 4 Evaporator fan ...
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1answer
80 views

Relationship between directional derivative and gradient in x, y and z

Can anybody explain the relationship between directional derivative and gradient? What can I use the results of directional derivative and gradient for ?
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40 views

Finding the total distanced covered (physics)

A subway train starts from rest at a station and accelerates at a rate of $1.60\frac{m}{s^2}$ for $14.0 s$ . It runs at constant speed for $70.0 s$ and slows down at a rate of $3.50\frac{m}{s^2}$ ...
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63 views

Integral over orthogonal cylindrical harmonics

I am unsure how to solve an integral equation. As you know the orthogonality relation for cylindrical harmonics is: $$ \int_0^{2\pi}e^{in\phi'}e^{-im\phi'}d\phi'=2\pi\delta_{m,n}\ $$ The problem I ...
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25 views

How to decompose a representation of $so(n)$ into representations of a subalgebra

In some cases, it is possible. For instance the representation $16$ of $so(9)$ decomposes as $8_c+8_s$ of $so(8)$. Now I would like to do the same with representations of $so(8)$ into a sum of ...
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61 views

Probably simple, but i don't get it

Now I was doing some physics and I got to this equation, task is solved but i don't get this part... So is it possible to get for $$\frac{m_1(v^2_1-w_1^2)}{m_1(v_1+w_1)}=w_2$$ to $v_1-w_1=w_2$.
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68 views

Asymptotic expansion of $\sum_{k=0}^{\infty} k^{1 - \lambda}(1 - \epsilon)^{k-1}$

I'm seeing a physics paper about percolation (http://arxiv.org/abs/cond-mat/0202259). In the paper the following asymptotic relation is used without derivation. $$ \sum_{k=0}^{\infty} k P(k) (1 - ...
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164 views

What went wrong?

Intrigued by this question, one-dimensional inverse square laws, I started to try to find an answer and came up with what follows. However, I calculated the derivatives to double check myself, and ...
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38 views

Simplify this expression?

I have the following expression $$\frac 12 x_0e^{-\beta t}\left[\left(\frac {\beta}{i \sqrt{\omega ^2-\beta ^2}}+1\right)e^{i \sqrt{\omega ^2 - \beta ^2}t}+\left(\frac {- \beta}{i \sqrt{\omega ^2 - ...
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125 views

About Null Electromagnetic Fields and Null Congruences of Geodesic Shear-free

It was proved that, in spinors representation, a null electromagnetic field determines a shear-free null congruences, namely "A spinor field $n_A$ such that $\phi_{AB}n^B=0$ is a shear-free null ...
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22 views

Hydrogenhamiltonian self-adjoint in one or two dimensions

let $d\in\{1,2\}$. I'd like to know if the operator $H=-\Delta - \frac{1}{|x|}$ is self-adjoint as an operator acting on a dense subset of $L^2(\mathbb R^d)$. In particular I'd like to know how its ...
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34 views

Size of square formed by soap in a cube frame

So through the work of Plateau (as I understand it), we know that soap tries to find the shortest connection between points. At least, that's what I was taught. With this in mind, I had to solve the ...
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1answer
36 views

Why are the uncertainties so different?

Here is my scenario: I am trying to calculate the uncertainty of the function $y=x^2$, that is, I want to find $\Delta y$, and I found that we can get a great difference in the $\Delta y$, depending ...
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170 views

Solution of the equation.

I have the following equation and I am interested in to find out the value of $r$, $(1-r)^3+3(1-r)h^2-3h(1-r)^2-\dfrac{wh^3}{KM}=0$ I simplified this equation to the following equation, ...
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56 views

Scalar Product Conditions

Let $x$ and $y$ be two vectors, $x\cdot y$ their scalar product, $\beta$ the angle between the vectors, and $|x|$ and $|y|$ their absolute values. Then we have $$|x| |y| \cos \beta =x \cdot y \quad ...
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57 views

Finding acceleration at a certain velocity

A race car starts from rest and travels east along a straight and level track. For the first $5.0s$ of the car's motion, the eastward component of the car's velocity is given by ...
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193 views

Find acceleration at the first instant when a car has zero velocity.

The position of the front bumper of a test car under microprocessor control is given by: $x(t)=2.17m+\left(4.8\frac{m}{s^2}\right)t^2-\left(.100\frac{m}{s^6}\right)t^6$ Find its acceleration at the ...
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1answer
35 views

Special Relativity Dilation problem

I've been given the following scenario: Observer $B$ is in the center of a train carriage which is moving at velocity $v$ with respect to an observer $A$. Two light signals are emitted from ...
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1answer
98 views

Transpose of the gradient of a vector field.

Whereas I understand what the gradient of a vector field means physically, I am having difficulty understanding what its transpose actually is. I came across it in the context of defining strain in ...
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104 views

How are Lagrangian mechanics equivalent to Newtonian mechanics?

I didn't study Lagrangian mechanics yet but I did study Newtonian mechanics, and someone said to me that later we would study analytic mechanics (which contain Lagrangian mechanics) and that it ...
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94 views

Integrate the product of two exponential functions

I am trying to solve the following integral: $ \int^{\infty}_{-\infty} \exp{-3/2L [(r^{(0)}- \epsilon)^{2} + \sum_{a=1}^{n}(r^{(a)}-\Lambda \epsilon)^{2}]} d^{3}\epsilon$ I have try to use the the ...
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1answer
33 views

Can you add potentials if charge redistributes?

Let say we have charged conductor $M$ and we know its potential energy function $V_m(r)$ when $M$ is isolated from any charges. We also have charged conductor $N$ with potential energy function ...
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1answer
142 views

SO(2) group generator Lie Algebra

For the $2 \times 2$ orthogonal group of matrices which for the $SO(2)$ group, there is only one free parameter in the group element and hence only one generator for the group. Which is, $$ X_g = ...
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85 views

What is the reason for normalizing eigenvectors?

In Linear Algebra, when we have found eigenvectos related to specific eigenvalues, we normalize the eigenvectors. If I want to normalize eigenvectors, why do I need to normalize the eigenvectors?
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1answer
65 views

proof of $\frac{\partial \frac{\partial f(x,y)}{\partial x}}{\partial y}=\frac{\partial \frac{\partial f(x,y)}{\partial y}}{\partial x}$

I was at my physics class(electrodynamics).I saw a relation which frequently uses in my course.Relation is that $$\frac{\partial \frac{\partial f(x,y)}{\partial x}}{\partial y}=\frac{\partial ...
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1answer
44 views

The “computability” of fundamental physical constants

I would like to ask if any of the fundamental physical quantities like the speed of light or plancks constant (all measured according to a common standard of of units) can be classified as computable ...
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2answers
31 views

Finding the magnitude of a vector product between two vectors?

Vector $\overrightarrow{A}$ has magnitude $11.0m$ and vector $\overrightarrow{B}$ has magnitude $16.0m$ . The scalar product $\overrightarrow{A}\bullet \overrightarrow{B}$ is $79.0m^2$. What is the ...
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3answers
63 views

Boxes on a slope [closed]

A box with friction slides down a slope and takes 2 times longer than a similar box with no friction takes to slide the same slope. What is $ \mu $ (the coefficient of friction)? I'm pretty lost. I ...
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28 views

Trying to understand free body diagram [closed]

Please consider the following image: Now I'm just trying to understand how exactly this thing is rotated...I'm looking at it exactly like on the image of the car...So the normal force is slightly ...
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3answers
75 views

Online resources for special relativity

I wasn't sure where to post this, but I'm on a mathematics course that has basically brushed over special relativity. I'm also doing an out of department module called philosophy of physics and as you ...
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54 views

Proving commutation relation in Algebraic Bethe Ansatz

I have a problem with proving a certain commutation relation. For my Bachelor's thesis I give a more mathematically rigurous 'treatment' of a select set of chapters of a paper by L.D. Faddeev. Noting ...
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1answer
180 views

Applications of infinity in real life [duplicate]

I am writing a mathematical essay and would like to focus on the concept of infinity. I am not sure of any real life applications of infinity to write about or some way to narrow down the topics. Does ...
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83 views

A simple physics related algebra question.

This is making me feel like an idiot. I'm given this answer for a question but I don't understand it. $$y =\rm (-12.9\, m/s)(3.27\, s) + 1/2(9.81\, m/s^2)(3.27\, s)^2 = 105\, m = 0.11\, km$$ I ...
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41 views

pierre simon laplace and his knowledge of the (Laplacian) matrices

so as we all know, there is a graph matrix called the Laplacian that is used in some eigenvalue/eigenvector/graph theory/spectral theory problems. i'm wondering if the name of this matrix is ...
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1answer
115 views

Generators of Translation - Lie Algebra [duplicate]

I have just started learning Lie Groups and Algebra. Considering a flat 2-d plane if we want to translate a point from $(x,y)$ to $(x+a,y+b)$ then can we write it as : $$ \left( \begin{array}{ccc} ...