Tagged Questions
0
votes
1answer
37 views
Finding the Extremals of a Functional J.
The functional $J$ is defined on smooth functions $y \colon [a,b] \to \mathbb{R}$ satisfying $y(a) = u$, $y(b) = v$ and is given by
$$J[y]=\int_a^b \sqrt{y} \sqrt{1+(y')^2}\, dx.$$
I have found ...
1
vote
3answers
59 views
How can you show that $\delta′=f(0)\delta′−f′(0)\delta$ for a function f that is infinitely differentiable?
Assume that $f$ is infinitely differentiable. Let $\delta$ be the (Dirac) delta functional.
I know that $f\delta = f(0)\delta$, but I'm not sure how to derive the equation ...
2
votes
1answer
60 views
Trouble understanding a common vector calculus example
I have difficulty understanding the following vector calculus example. Text can be found here. It is the 5th Q&A -- starting with equation (31.1035).It concerns finding the vector potential of a ...
-1
votes
0answers
34 views
Chain Rule Problem [closed]
Newton's Law of Gravitation asserts that the magnitude of force between objects of masses $M$ and $m$ is $F = GMm/r^2$ where $r$ is the distance between them and $G$ is a universal constant. Let an ...
5
votes
1answer
78 views
Degree of maps on the 3-sphere
I am currently in the process of going through Ticciati's Quantum Field Theory for Mathematicians, which states the following (Theorem 13.7.11):
"Let $g$ be a differentiable function from $S^3$ to a ...
0
votes
1answer
52 views
Calculating the angular velocity
I have an inverted pendulum with a accelerometer mounted on the top that at rest gives me a vector up opposite to gravity, which is used to calculate the angle of the pendulum. Is it possible to ...
0
votes
1answer
93 views
Nonlinear Second-order ODE BVP with 4 boundary conditions
My Lagrangian comes out in this form when I impose spherical symmetry:
$$ φ''(ρ)+{3\overρ} φ'(ρ)+{4μ^4\over M^2} φ(ρ)-{4μ^4\over M^4} φ^{3}(ρ)-{μ^4\over2M} ϵ=0 $$
The following boundary conditions ...
1
vote
1answer
28 views
Are there solutions when the boundary conditions are particle positions at 2 different times instead of positions and speeds at an initial time?
Is it possible to find solutions for a dynamic system when the boundary conditions are particle positions at 2 different times instead of positions and speeds at an initial time?
The question is ...
0
votes
0answers
27 views
Using the integral equation, find the eigenvalues and eigenfucntions
The integral equation:
$$
\int_{-\frac{T}{2}}^{\frac{T}{2}}dt' \phi (t')e^{\Gamma\left | t-t' \right |} =\lambda \phi(t)
$$
for $(-\frac{1}{2}T< t < \frac{1}{2}T)$
is useful in photon ...
1
vote
1answer
22 views
Is this a set of generators for the conformal group of Minkowski space?
My physics textbook asserts that the group of maps $f: M \rightarrow M $ ($M$ is the Minkowski space, i. e. $\Bbb R^4$ with the pseudonorm $||x||=x_0^2-x_1^2-x_2^2-x_3^2$ and scalar product $x\dot{} ...
1
vote
2answers
41 views
Units in this problem: velocity or distance?
I know this is slightly off-topic here, but it's really bothering me.
My class was given the following immensely simple problem today:
A bird flies due south at a constant speed of ...
0
votes
1answer
34 views
Observer in magnetic and electric fields
respect an inertial observer O, I have an object of weight m and charge $q$. It is in a electric field $E=(E,0,0)$ constant and a magnetic field $B=(0,0,B)$ constant. I have another observer o' that ...
1
vote
0answers
28 views
Three body problem with point interactions
I've studied the HVZ theorem for the three body problem interacting with regular potentials. I'd like to extend this result to the three body problem with point interactions (delta potentials).
Is ...
2
votes
1answer
59 views
Determine the Fourier Transform and Fourier Series of the function
$$
f(t)=\frac{\sin(at)}{t}
$$
Since the term is parameterized, it's easy to see that if I take the first derivative with respect to 'a', then the function becomes considerably easier. I do this to ...
0
votes
0answers
60 views
Translation of an article
I need to read this article
"On the spectrum of an energy operator for atoms with fixed nuclei in subspaces corresponding to irriducible representations of permutation groups"
authors:G.Zhislin, A. ...
4
votes
3answers
138 views
Physics notation justified
Sometimes in physics they do things like this one:
If $dq=f\left(x\right)\cdot dr$ then $\frac{dq}{dt}=f\left(x\right)\cdot \frac{dr}{dt}$
Which mathematically is a wrong deduction. Is there any ...
1
vote
0answers
25 views
References for three body problems with Fermi statistic
I'm studying the three body problem with two fermions of unitary mass and another different particle. I need references of the HVZ theorem in this case. Is there someone who knows them?
1
vote
1answer
65 views
Does a constant of motion always imply hamiltonian?
If a dynamical system has a constant of motion, and is not already evidently Hamiltonian, is it always possible to use a change of variables and obtain a Hamiltonian system?
Edit: the constant of ...
2
votes
0answers
63 views
Solving Generalized Eigenvalue Problem perturbatively
Let me formulate the problem to convey my notation.
I have a matrix $A$ which is hermitian - and is diagonalisable by a transformation
$$ U_A A\,\,U_A^{-1} = A_{diag}$$
Now the matrix is changed, ...
0
votes
0answers
32 views
Solvable Models In Quantum Mechanics
Is there anyone who studied on the book "Solvable Models In Quantum Mechanics" by Albeverio? I don't succed in understanding the proof of page 116 about the eigenvalues of the Hamiltonian with point ...
-1
votes
1answer
58 views
Searching for an article [closed]
Is there anyone who knows where can I find this article:
"On the spectrum of an energy operator for atoms with fixed nuclei in subspaces corresponding to irriducible representations of ...
0
votes
2answers
78 views
Vector Analysis (Phasor-diagrams) of poly-phased circuits
I have a poly-phased circuit of $q$ phase ($q$ input voltage in equilibrium) such that $$1\le i \le q, \quad V_i= V_{max}\sin\left(\omega t - (i-1)\cfrac {2\pi}{q}\right) $$
How can I use vector ...
2
votes
0answers
75 views
Mathematical significance of the “Dirac conjugate”
Let $\psi$ be a Dirac spinor. The so-called "Dirac conjugate" of $\psi$ is defined to be $\widetilde{\psi}:=\psi ^*\gamma ^0$, where $^*$ denotes the adjoint and the gamma matrices $\gamma ^\mu$ ...
0
votes
0answers
64 views
Hermitian conjugation and representations of the Lorentzian Clifford algebras
The Clifford algebra $\mathcal{C}\ell _{1,2d-1}$ is central and simple (L), and hence has a unique faithful, irreducible representation (over $\mathbb{R}$) (A). Denote this representation by $\gamma ...
4
votes
1answer
65 views
Existence Energy of Wave Equation
I was just going trhough some properties of the wave equation, including the energy of the wave equation given by $E(t)=\int_{-\infty}^{\infty}u_t^2+c^2u_x^2 dx$, i.e the sum of kinetic and potential ...
1
vote
1answer
208 views
Energy of wave equation decreasing
I have problems checking that the energy $E(t)=\frac{1}{2}\int_I(u_t^2+c^2u_x^2)dx$ on an open interval $I\subset \mathbb R$, such that $u(0,x)=0$ and $u_t(0,x)=0$ for $x\in\mathbb R\setminus I$ is ...
2
votes
0answers
77 views
How to convert a hologram into an image?
Suppose one knows in full detail the phase and intensity of monochromatic light in a plane. This is basically what a hologram records, at least for some section of a plane. By using this as the ...
0
votes
1answer
96 views
concise review of Maxwell's electromagnetic equations for math students
I am a graduate student in applied mathematics and I am looking for a concise introduction to Maxwell's equations / basic principles of electromagnetism. (I have enjoyed the book by Purcell, ...
1
vote
1answer
102 views
P-adic Numbers and Eternal Inflation
In October(??) 2011, Leonard Susskind gave a talk and with few other people wrote a paper about P-adic numbers and measure problems(??) in cosmology. Has there been any recent talks, papers, ...
4
votes
2answers
212 views
$SU(2)$ Representation of $SO(3)$
I've often seen it written that $SU(2)$ is a "two-valued representation" of $SO(3)$ (in theoretical physics books mainly). I have a major conceptual issue with this however.
I know there is a Lie ...
1
vote
1answer
91 views
Discontinuity of double-layer potentials
I'm currently reading about solutions to boundary-value problems for Laplace's equation, and I'm a bit confused with regards to the discontinuity properties of double-layer potentials. So the text ...
1
vote
2answers
406 views
Derivative of position is velocity and of velocity is acceleration?
This is more of a personal question (i.e. not school related), but how has it been proven that the derivative of position is velocity and derivative of velocity is acceleration? I did some Google ...
0
votes
2answers
85 views
What do I need to read to understand dimensions and spacetime?
The concept of dimension seems to be:
In physics and mathematics, the dimension of a space or object is
informally defined as the minimum number of coordinates needed to
specify any point ...
0
votes
2answers
90 views
Show that the following cycle has a limit cycle
By direct calculation show that (using polar coordianted) that
$$
\dot x=x-y-x(x²+y²)
$$
$$
\dot y=x+y-y(x²+y²)
$$
Show that this has a limit cycle
I need help understanding how to test whether it ...
0
votes
1answer
84 views
Which of the following is gradient/Hamiltonian( Conservative) system
The question that I have to solve is found below. However, I do not know how to start the solution since I am unsure about the defintion of a Gradient/Hamiltonian System. What must I check first to ...
0
votes
0answers
121 views
sinusoidal word problem
in tidal waves the sea level drops first leaving the seabed exposed (normally 30 feet below sea level), then it rises a equal distance above sea level. waves hitting a city have a max height of 38.9 ...
0
votes
1answer
186 views
damped wave equation
For $t>0$, $x$ in a compact Riemannian manifold $(M,g)$, and $a\in C^\infty(M)$, $a\geq0$, $(\partial_t^2+a\partial_t-\Delta_g)u=0$ is called the damped wave equation.
My question is...why is the ...
0
votes
1answer
170 views
A integral equation generated from current density distribution in a wire
Consider a wire carrying a current $I$, I need to find the current density distribution in the wire of a cylinder shape. Let the density function be $j(x,y)$, in the circle $D:x^2+y^2<r^2$.
We ...
6
votes
1answer
186 views
What is quantum field in terms of mathematics?
I am reading a book on quantum field theory, while I have never been trained as a physicist. I found a big gap in language and have trouble understanding what physicists mean by "quantum field".
If I ...
1
vote
0answers
66 views
Wilson lines, boundary condisions, surface defects of TQFTs
I have been studying (extended) topological quantum field theories (in short TQFTs) from the mathematical point of view and I have no background of the physics point of view. Sometimes I encountered ...
1
vote
1answer
74 views
Difference in sound between a string and a pipe
I am told that I can model the vibration of a guitar string of length $l >0$ by the following Sturm-Liouville equation
$$ -u'' = \lambda u \: \: \text{ on } [0,l],$$
with boundary conditions
...
0
votes
1answer
38 views
What is $\left(\delta_{ab}\right)^{-1}$?
I have an expression that involves the Wigner 3j coefficient:
$$\left(\matrix{a&b&0\\0&0&0}\right)^{-1}$$
This simplifies to:
...
1
vote
1answer
48 views
How to linearize $V=V_w+(V_0-V_w)e^{-kt}$
I have a physics homework and I was asked to transform $v=v_w+(v_0-v_w)e^{-kt}$ into a linear equation to be graphed. ($v_w$ is one variable that is constant and $k$ is constant.) $v$ is velocity ...
1
vote
0answers
57 views
Differential equations with different constants for different sub-domains
I remember that when I was studying differential equations, there was an example with solutions of the form $f(x) + C_1$ for $x>0$ and $f(x)+C_2$ for $x<0$ where $C_1$ and $C_2$ may be different ...
7
votes
1answer
336 views
Does apparent retrograde motion of planets begin and end at quadrature?
I've read it several places that the apparent retrograde motion of planets (during which they seem, as viewed from Earth, to move in the opposite sense of their normal "direct" orbital motion against ...
0
votes
0answers
43 views
When can I treat vectors as regular variables when differentiating?
Given this Lagrangian where $\dot{\vec r} = \left(\dot x, \dot y, \dot z\right)^T$:
$$ L = \frac m2 \left|\dot{\vec r}\right|^2 - q \left( \phi - \left\langle \dot{\vec r}, \vec A \right\rangle ...
0
votes
1answer
61 views
Yet another differential equation
Hello,
I would appreciate any help solving the following equation:
$$\begin{align}
y''[t] + \dfrac{d}{m}y'[t] + \dfrac{k}{m}y[t] = G \\
\end{align}$$
subject to:
$$t[0] = t0$$
$$t'[0] = 0$$
This is ...
3
votes
2answers
107 views
Help solving differential equation
I want to solve the following differential equation:
$y[t]$ : vertical position (height) of the object at time t
$y_c$ : height of the ceiling
$y_e$ : equilibrium point, the height at which the ...
-4
votes
1answer
56 views
The proper way to find standard error [closed]
I had a lab where calculating standard error was explained. My instructor did a cross multiplication move and ended up with range / n
How exactly does this work?
Are there other ways of representing ...
4
votes
4answers
191 views
Applications of Operator Algebras to modern physics
I think that recently I've started to lean in my interest more towards operator algebras and away from differential geometry, the latter having many applications to physics. But while taking physics ...
