"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
0answers
23 views

a group of order 32

Consider the creation and annihilation operators $\left\{a_{1},a_{2},b_{1},b_{2}\right\}$: $$[a_{i},a_{j}]_{+}=0,[b_{i},b_{j}]_{+}=0, a_{i},b_{j}]_{+}=\delta^{j}_{i}$$ with ...
3
votes
1answer
62 views

What is mathematical equation of the Gravitational force between three objects?

This is mathematical equation of the Gravitational force between two objects: $$F_G=\frac{GM_1M_2}{r^2}$$ what is mathematical equation of the Gravitational force between three objects?
8
votes
1answer
173 views

Topological Quantum Field theories

I was wondering about the following on TQFTs. It is said that TQFTs have vanishing Hamiltonians $\hat{\mathcal{H}}$. Firstly, I would like to ask: Why is this so? Secondly, consider the ...
-1
votes
3answers
51 views

Why gauss's law of gravity has negative sign?

Why Gauss's law of gravitational field have negative sign but gauss's law of electric field is positive sign? $$\nabla\cdot{\bf{g}}=-4\pi \rho G$$ $$\nabla\cdot{\bf{E}}=\frac{\rho}{\epsilon_0}$$
0
votes
0answers
16 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 ...
1
vote
0answers
49 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 ...
1
vote
0answers
25 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 ...
2
votes
0answers
39 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 ...
0
votes
0answers
13 views

Difference between Maximum Likelihood Estimation and Baysian Probability Estimation

I 've heard there are two parameter estmation methods, such as, MLE and BPE. How can I distinguish the two parameter estimation methods?
2
votes
1answer
39 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 ...
0
votes
0answers
28 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 ...
1
vote
1answer
43 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 ...
0
votes
0answers
40 views

Find sufficient and necessary conditions such that the solution $u$ of this PDE is unique

Let us consider the following PDE probem: $$Δu(x,y)=\frac{\partial^2u(x,y)}{\partial x^2}+\frac{\partial^2u(x,y)}{\partial y^2}=0, (x,y)∈(0,1)\times\mathbb{R}$$ $$u\left(\frac{1}{2},y\right)=0, ...
2
votes
0answers
30 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 ...
0
votes
1answer
34 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.
0
votes
1answer
31 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 ...
0
votes
2answers
46 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 ...
2
votes
0answers
30 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) = ...
0
votes
1answer
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 ...
3
votes
1answer
131 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 ...
1
vote
2answers
19 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 ...
1
vote
1answer
42 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 ?
0
votes
3answers
37 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 $3.50\frac{m}{s^2}$ ...
2
votes
0answers
51 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 ...
0
votes
0answers
18 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 ...
2
votes
1answer
60 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 $v_1-w_1=w_2$.
3
votes
2answers
59 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 - ...
6
votes
3answers
160 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 ...
0
votes
1answer
34 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 - ...
0
votes
0answers
104 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 ...
0
votes
0answers
20 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 ...
0
votes
1answer
30 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 ...
1
vote
0answers
40 views

Generalization of the identity $\int_{\mathbb{R}}e^{-x^2}H_n(x+x_1)H_n(x+x_2)\;dx=2^n n!\sqrt{\pi}\, L_n(-2x_1x_2)$

Apparently there exists an integral identity relating Hermite and Laguerre polynomials: $$\int_{\mathbb{R}}e^{-x^2}H_n(x+x_1)H_n(x+x_2)\;dx=\sqrt{\pi}\cdot n!\cdot 2^n\cdot L_n(-2x_1x_2).\tag{1}$$ Can ...
1
vote
1answer
35 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 ...
0
votes
0answers
98 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, ...
0
votes
1answer
30 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 ...
1
vote
1answer
36 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 ...
0
votes
1answer
85 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 ...
3
votes
1answer
32 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 ...
0
votes
1answer
36 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 ...
0
votes
1answer
63 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 ...
0
votes
0answers
76 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 ...
0
votes
0answers
30 views

Mathematic Model Based newton Law [modelling math]

lower mathematical model By making use of Newton's laws, lower the mathematical model The following mechanical systems. Provide sufficient explanation of the phenomenon occurs. sorry for my bad ...
1
vote
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 ...
1
vote
1answer
55 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 = ...
1
vote
1answer
62 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?
1
vote
1answer
61 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 ...
2
votes
1answer
39 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 ...
1
vote
2answers
25 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 ...
0
votes
3answers
54 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 ...