"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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Dimension of $\left(\lambda |\psi\rangle \langle\psi| +(1-\lambda)\frac{\mathrm{I}}{2}\right)^{\otimes N}$

I have the $N$-fold tensor product of a convex combination of a pure state, i.e. $|\psi\rangle\langle\psi|$ with $|\psi\rangle$ a unit vector in a complex Hilbert space of dimension two, and the ...
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1answer
71 views

Easy classical physics made mathematically rigorous!

Consider the following: We are given a symplectic manifold $M$. Now, we define a Hamilton function $H : M \rightarrow \mathbb{R}.$ Additionally, we want that $H^{-1}(x)=:M_x$ is a submanifold. We can ...
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2answers
42 views

Three cyclists Raman, Mohan and Nitin ride around a circular course

Three cyclists Raman, Mohan and Nitin ride around a circular course 85 km around at the rate of 8, 12 and 20 km an hour. Raman and Mohan ride in the same direction and Nitin in the opposite direction. ...
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1answer
38 views

Affinity of lorentz transformations

Lorentz transformations are often defined to be linear. But suppose instead we only consider transformations that preserve the spacetime interval. Is it possible to prove that those transformations ...
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31 views
+50

Given a transformation, find the generating function

There's a mapping $(x,y) \mapsto(u,v)$ given by $u= x\cos\theta-y\sin\theta$ $v =x\sin\theta + y\cos\theta$ I'd like to find a generating function $G(x,y)$ for this mapping, which I understand to ...
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1answer
37 views

Intuition behind surface integrals

While line integrals derive their intuition from , and are analogous to, the concept of Work in physics, what intuition is there to back up the notion of surface integrals? In the texts I've been ...
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27 views

Thermodynamics based proofs

What are some mathematical inequalities and theorems that follow using thermodynamics "proofs" (rigorous or just intuitive)? Any suggested books on the matter? For example, AM-GM inequality follows ...
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17 views

Gaussian unitary dilation of Gaussian channels

I am starting with a few definitions. All these are standard and can be accessed from some quantum information or quantum physics books, for instance the books by Holevo or Parthasarathy. The question ...
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2answers
31 views

Physics- projectile motion. Given values: time of flight and horizontal component velocity. Ball launched at an angle returning to the same height.

A person throws a baseball with a horizontal component velocity of 25m/s. It takes 3 seconds to come back to its original height. Calculate its horizontal range, its initial vertical component ...
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40 views

What is elnekiti's triangle? (edited) [closed]

Elementary ceĺular automata shows amazing complex systems such as pascal's triangle is similar to " wolfram rule 90 " , so i looked over youtube searching for extra content and i found this video Here ...
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12 views

Modeling smoke cloud as expanding Gaussian / ellipse

I am making a simplified model of smoke coming from a train's smokestack. You can imagine that if you want an accurate model you have to think in 3D and use computational fluid dynamics and stochastic ...
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1answer
28 views

The literature on Chern-Simons theory

Can any one give some literature on Chern-Simsons theory? I can not find any book introducing this theory. Thanks.
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1answer
41 views

What is $\mathrm{dim}(\mathrm{Sym}(\mathrm{Herm}(H)^{\otimes N})$?

The totally symmetric subspace of $(H^k)^{\otimes N}$, with $H^K$ a $k$-dimensional Hilbert space, has dimension $\binom{N+k-1}{k-1}$. But I now want to know the dimension of the totally symmetric ...
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1answer
27 views

Couple stress tensor reference.

Can someone give me a good mathematical reference for couple stress tensor in its most basic form. Thank you.
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14 views

Heat equation with $x\in [0,+\infty[$ and non-homogeneous initial and boundary condition

The IVBP that i need to solve is the follow: \begin{equation} \begin{cases} u_t=au_{xx} & x>0,t>0,a\in\mathbb{R}^+\\ u(x,0)=B_0e^{-kx}\cos(kx) & x\geq ...
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1answer
19 views

How to calculate $e^{ad\hat{A}}\hat{B}$?

For $\hat{a}$ and $\hat{a}^{\dagger}$ is annihilation and creation operators which, $[\hat{a},\hat{a}^{\dagger}]=1$. Could you please show me the way to calculate, ...
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106 views

What comes under Mathematical Physics. [closed]

Suppose Math has 5 sub parts: Analysis: Analysis, Complex Analysis, Measure theory and integration,Functional Analysis Algebra: Group Theory, Vectors space-rings-modules, Galois, Algebra Number ...
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1answer
24 views

Hamiltonian vector field and symplectic geometry

I want to show the following theorem: For any Hamilton function $H : M \rightarrow \mathbb{R}$ on some symplectic manifold $M$ and symplectomorphism $f : M \rightarrow M$ we have $X_{H \circ f} = ...
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1answer
33 views

Defining a partial derivative with respect to an antisymmetric tensor/matrix

I'm looking at some nonlinear electrodynamics, and have been following a textbook which contains a primer on some of the stuff I'm interested in following up. However, I seem to have fallen at the ...
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1answer
30 views

Impact of two bodies problem

A body of mass $M$ moving with a velocity $u$ collides with another of mass $m$ which rests on a table. Both the balls are perfectly elastic and smooth and the the body of $m$ is driven in a ...
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0answers
28 views

Stability of ground state under positive (not relatively bounded) perturbations

This is about positive perturbations that are not necessarily relatively bounded, but where the perturbed operator is known (by some independent proof) to be self-adjoint. Is this a known result (or ...
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2answers
104 views

What is the most general notion of “Fourier transform?”

I know the definition of a classical Fourier transform that maps a function f(x) on the real line X to a function F(p) on a dual space (here another real line and borrowing some physics notation) P. ...
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3answers
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What's the name of this theorem?

It happens very often in physics that we find relations like: $$\int_V f(x) dx = \int_V g(x) dx$$ for an arbitrary volume $V$. From this we usually say "Since the volume is arbitrary, the integrands ...
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39 views

Vector Calculus - Polar Co-ords

I am having a lot of difficulty finding an approach to solving the following question: A dyon is a particle with both electric and magnetic charge; in suitable units $$\mathbf{E} = ...
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27 views

Conformal field theories and critical points

I apologize in advance if this question belongs to physics.stackexchange. I've been trying to learn CFT following Zee for QFT background (approximately first and second chapter,) and then Di ...
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1answer
20 views

What set of straight ramps exist such that a ball sliding down any one of them would reach the base at the same time?

I'm looking for a set of straight ramps, which, under idealised conditions (uniform gravitational acceleration and no friction) would have a point-like body slide down them from the top to the base ...
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1answer
49 views

Is there an analytic or at least a numerical solution to an eqaution of the form $\sqrt{k_1\sqrt{x}+k_2}\;\Big(k_3x+k_4\sqrt{x}+k_5\Big)+k_6=0$?

So the problem comes from cosmology and I want to solve for the unknown function $a(t)$, which is the scale factor for the universe. So I have an integral involving $a$: $$ ...
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1answer
26 views

Deflection - irradiation direction.

Compute the beam deflection $\delta$ (see figure) through a prism with angle $\epsilon$ as in the figure and refractive index $n_p$. When is the deflection $\delta$ minimal compared to the original ...
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1answer
13 views

Glass prism - refractive index

Light falls perpendicular on one side of a glass prism with refractive index n. The light is totally reflected on the right side. 1.1: Determine the angle of incidence using the figure ...
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1answer
54 views

Stuck on computing distance travelled from velocity and yaw rate.

I am somewhat stymied on what appears to be a simple formula. Here is the problem statement: Assume that a rigid body is traveling with constant velocity $v$, and is rotating with a constant yaw rate ...
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7answers
773 views

Why does the “separation of variables” method for DEs work? [duplicate]

Heyho, I am using the separation-of-variables method for quite a while now, but what was always bothering me a bit, is why is it possible to do those operations. I'll give a concrete example (source ...
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2answers
103 views

Is the following PDE boundary value problem well-posed?

My Question Is the following Poisson boundary value problem well-posed, as stated? If so, how could I go about solving it? If not, what would it need to be well-posed? Does it satisfy the ...
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1answer
20 views

Inclined plane - euler-lagrange

A mass point of mass m moves frictionlessly down an inclide slope under influence of gravity. Solve the equations of motion and determine the constraint with the use of the lagrange equation of ...
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42 views

Euler-Lagrange - circle cone

A mass point moves on the wall of a hollow circle cone under influence of the homogeneous gravitational field of earth. Use spherical coordinates to solve this problem. a)Set up the ...
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21 views

Possibly use a Fourier Transform to perform deconvolution

I need to determine the function g(B) in order to determine its prefactors $a_n$. Here's what I have: h(f,B) is a Gaussian function g(B) is the unknown function i(f) is an inhomogeneous function and a ...
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1answer
59 views

Equation of motion - curve - particle

A particle of mass m moves frictionlessly under the influence of gravity on a curve defined by: $x=a(\phi+\sin\phi)$ and $y=a(1-\cos\phi)$. a) Set up the terms for the kinetic and ...
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trace calculation of an operator valued matrix

Heyho, i've got problems understanding a certain calculation of the trace of an operator valued matrix right now. We've got the Matrix $T(\lambda)= \begin{pmatrix} A(\lambda) && B(\lambda) ...
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37 views

Determining the group generated by a set of roots?

I have a set of 45 roots and I want to know which group is generated by the corresponding generators. In the set are 5 diagonal (=Cartan) generators $$ (0, 0, 0, 0, 0, 0)_1,(0, 0, 0, 0, 0, 0)_2,(0, ...
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1answer
88 views

$A^tA-AA^t$ in Mathematical Physics

In very different contexts of mathematical physics (rigid body mechanics, fluidodynamics, general relativity, quantum field theory,...) I have come across the following expression: $$ A^tA-AA^t, $$ ...
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1answer
19 views

Complex refractive index.

A linearly polarized wave with the vacuum wavelength $\lambda_0$ falls perpendicular on a material with the complex refractive index $\bar{n}=1.5+i\cdot 0.15$ with that wavelength. After what ...
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3answers
63 views

Figure out the component of a value in X and Y coordinates using trigonometry.

Alright. It's been long that I studied trigonometry and did Laws of Motion and Free Body Diagrams, and I was decent good at them, but somehow I am having trouble in understanding the following. Note ...
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8 views

Refractive index - medium

To determine the refractive index of a medium two identical em-waves are generated. One wave goes through unknown medium whereas the other one stays in vacuum. Determine the refractive index ...
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0answers
50 views

A problem on Constrained Motion

Q. A particle is moving in a smooth curve under gravity and its velocity varies as the actual distance from the highest point. Prove that the curve is a cycloid. Attempt: The eq. of motion is ...
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1answer
29 views

solving equation in terms of $w_1$ and $w_2$

I have a a physics problem involves the following equation $$\tan(\alpha) = \frac{(w_1 + w_2)^{1/2}}{w_3}$$ from a certain set of equations that I use I derive the following equation: ...
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2answers
60 views

Practical use for negative $dt.$

I am writing a section of notes for Calculus 1 on related rates. In the section where I discuss differentials, I write that the quantity $dt$ must be nonnegative. I imagined the only reason it would ...
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1answer
65 views

What's wrong with my math in this function to update the position of a planet near a star?

Initially the code seems to work as the planet curves toward the star, but then as it should either get pulled into the star or make an orbit, it just gets pushed away in the opposite direction. What ...
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1answer
31 views

Why is not parity transformation just a rotation?

I'm a bit confused about parity transformations (reflections). A parity operator $\pi$ takes a vector $(x, y, z)$ to $(-x, -y, -z)$. So in a $3$ dimensional space this takes a vector and points it ...
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Can someone help me to understand this formula.

Im trying to implement this in code, but I'm having some difficulties to understand it. • Using precalculation: $$\exp\left(-\frac{T}{T_f}\right) = 1 - \frac{T}{T_f} + ...
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47 views

Problem of Arnold's book and covering spaces

I am currently reading Arnold's book "Mathematical Methods of classical mechanics" on page 278 and I don't see through his arguments there at a point. Especially, I am talking about the part that ...
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24 views

Particle on a hemisphere - lagrange

A particle of mass m is on top of a frictionless hemisphere centered at the origin with radius $R$. It starts sliding down the hemisphere. Set up the lagrange equatinos of the first kind and ...