"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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Using index notation

I'm trying to work out the following, but have gotten myself a bit confused I'm still getting to grips with using indices: if I have $$\bar{\nabla} \times (\bar{a}\bar{x})\bar{b}$$ I re wrote this ...
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59 views

Force between two parallel wires?

Having two current carrying (currents $I'$ and $I$) wires of length $a$ parallel to the $z$-axis, one with end points $(0,0,0)$ and $(0,0,a)$ and one from $(a,0,0)$ to $(a,0,a)$, I'm looking for the ...
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4answers
75 views

Multiple choice question on rates of change (or so I thought)

If I were to find the resistance of the component (see image below), I would either find the equation of the curve and use differentiation or I'd draw a tangent at $V_2$ and then find the reciprocal ...
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1answer
28 views

Proving $\mathbf{E}$ and $\mathbf{B}$ satisfy Maxwell's first equation

Consider a scalar potential $\phi$, a vector potential $\mathbf{A}$, an electric field satisfying $\mathbf{E}=-\mathbf{\nabla}\phi-\dfrac{\partial}{\partial t}\mathbf{A}$, and a magnetic field ...
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32 views

Angular momentum, rotating rigid bodies, simple example…

Revising, this is what I'm stuck on: inertia tensors, rotating rigid bodies about axis other than its axis of symmety,... I think it'd help a lot to see a worked example and I can't find anything on ...
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1answer
138 views

Why study Bergman Spaces?

I'm interested in Operator Algebras and mathematical physics; recently, a friend showed me Duren and Schuster's "Bergman Spaces". I've read about two chapters now and I see there is a nice play ...
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15 views

Separation of the centre of mass coordinates for an N-electron atom

Can anyone tell me how to derive [A8.5] and [A8.6] in Appendice 8 of "Bransden: Physics of solid state matter", in this screenshot: http://i.imgur.com/zSCkVnI.jpg ? It should be easy, but damn me I ...
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26 views

Angular momentum, rotating cylinders,…

Revising, this is what I'm stuck on: inertia tensors, rotating rigid bodies about axis other than its axis of symmety,... I think it'd help a lot to see a worked example and I can't find anything on ...
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3answers
28 views

find a base to U Linear Algebra

dear users please help me... im answering a long question now ive been guided to find a base to U at the end of the process i got this $u= Sp\{x^4-3x^3+2x^2, 3x^4-7x^3+4x ,1\}$ and ive been guided to ...
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46 views

Polchinski 12.3.22 - superspace green's function

Forming the supersymmetric string using superfields and superspace, Polchinski claims that the function $$ G \sim \ln{\left|z_{1} - z_{2} - \theta_{1}\theta_{2}\right|^{2}} $$ satisfies the equation ...
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23 views

Decay for the solution of Hartree equation

Given \begin{equation}\frac{1}{i}\partial_t\phi-\Delta\phi=-(|x|^{-1}\ast|\phi|^2)\phi,\quad x\in\mathbb{R}^3,\end{equation} do you know of any result on the decay rate of ...
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32 views

Manifolds and magnetic potential

Assume we have a particle in $\mathbb{R}^3$, which we will subject to different fields independently. It will have some potential energy $U\in \mathbb{R}$ defined as some constant minus its kinetic ...
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1answer
20 views

Estimating curvature of oscillatory curve based on global constraints

I have a heuristic question about using global constraints of a problem to make estimates of local features of a curve, such as its curvature. Consider a suitably well behaved function on ...
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0answers
38 views

Meaning of this differentiation operators

I have been just reading this paper here: paper and was wondering how they carry out the differentiation in (4.9). In principle, this should be just the differentiation of 4.8 with the help of 4.7a. ...
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13 views

Center of Mass Coordinates

Can one view changing to center of mass coordinates http://www.worldforge.org/project/newsletters/July2002/LagrangianP3 as a kind of coordinate transformation in the same way one views changing ...
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1answer
33 views

Cross-Validation

Does anyone understand the paragraph below? The paragraph comes from Cross-valiation explanation at wikipedia. "It can be shown under mild assumptions that the expected value of the MSE for the ...
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1answer
194 views

Stoping time of light and photography [closed]

When taking a photo with a camera in manual mode, one needs to set the focus, the shutter speed and the exposure. The latter is controlled by adjusting the size of aperture, the circular opening that ...
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2answers
130 views

Why are 'differential operators on manifolds' differential operators?

It is clear what is meant by a differential operator on $\mathbb{R}^n$ (or some open subset). However, it is not clear to me why differential operators on smooth manifolds are defined the way they ...
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1answer
80 views

Bound on specific L2 function

Its stated in a paper by E. Lieb that this function is "clearly" in L2 $w(x)=|x|^{-1} - (g^2*|x|^{-1}*g^2)(x)$ with $g(x)=\xi^{3/4} \exp(-\pi \xi x^2/2)$ and therefore $||g||_2 =1$. It's ...
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1answer
34 views

Delta distribution - integration by parts of its differentiation

Some delta distribution physicist calculus. Assume there is given $$ \int_{\mathbb{R}^3} \sum_i f(\mathbf{x}) \delta^{(3)}(\mathbf{x}-\mathbf{a}_i) \ d^3x $$ with $f$ vanishing at infinity and ...
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0answers
41 views

Eigenvalues for the double-well potential

I am trying to find eigen-values, $E$, for the following differential operator: $$\left[ -\frac{1}{2}\frac{d^2}{dx^2} +L\left(x^2-a^2\right)^2\right]y(x) = E\,y(x) $$ where $L,a$ are two positive ...
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25 views

plane wave move out

I have a plane wave that is recorded by a set of receivers with x spacing between them (see the sketch). in the sketch (plane wave in black slant line, receivers are the little circles in black and ...
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15 views

Can multimodality exist in the absence of deterministic multistability?

I am not sure if this is the right SE to ask this question; it is about mathematical models for chemical reactions. I came across an article that says that multimodality of biochemical species can ...
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1answer
35 views

How to proof Frobenius Theorem in general?

The general Frobenius Theorem stating that Let $u_1,\dots,u_k$ be $k$ smooth linearly independent vector field on $M$. Let $$ W=\operatorname{Span}(u_1,\cdots,u_k) $$ Then $[u_i,u_j]\in W$ for ...
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1answer
61 views

Fourier-Laplace Transform of Heaviside Step function multiplied to Sine

In a Advanced Solid State lecture I encountered the following assertion- Fourier Transform of $\Theta(t)\sin(\omega_0 t)$ is ...
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2answers
40 views

Schrödinger-Operator on $L^2[0,2\pi]$.

In Reed-Simon Analysis of Operators they often talk about operators like $H = - \Delta +V$ as an operator on $L^2[0,2\pi]$ (like in Theorem XIII 88. What do they mean by that? Or is their a canonical ...
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0answers
27 views

Green's function the way George Green defined it

This is a curious question about the way George Green could have defined his Green's function. All the definitions I see have only Dirac-delta $\delta(x-x')$ function as their source on the RHS. But ...
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1answer
62 views

Uniform Circular Motion with Banked Road and Car

In Uniform Circular Motion, if a car is rounding a curve at a certain speed, and the angle of the road allows the car to drive around at that speed, that speed is called the "design speed." If the ...
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23 views

Is it possible to simulate fluid dynamics in a time-based and deterministic manner?

The Problem Domain I have a number of network-connected PCs. I want to be able to simulate and replicate the same simple fluid dynamics simulation (Eg Navier-Stokes), in real-time, between them. That ...
2
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1answer
79 views

Very strange “fact” regarding movement

Perplexing (for me at least) statement from the site: http://www.quora.com/Mathematics/What-are-some-of-the-most-counterintuitive-mathematical-results "Fact: You can have a car stand still for ...
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3answers
101 views

Compute the integral $\int_0^\pi \frac{\sin x}{x}dx$ .

How to compute precisely the integral $$\int_0^\pi \frac{\sin x}{x}dx$$ analytically? It is well-known that $$\int_0^{+\infty}\frac{\sin x}{x}dx=\frac{\pi}{2}.$$ One way to compute the above integral ...
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1answer
47 views

Solving Simplified Hamilton's Equation

I have a question on a project that I am working on. I have included a large amount of the background information so that all relevant information is included, however the question is as follows (it ...
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1answer
81 views

Learning Advanced Mathematics

I'm a 12th grade student and I've recently developed a passion for mathematics . Currently my knowledge in this particular area is comprised by : single-variable calculus , trigonometry , geometry , ...
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1answer
54 views

General relativity from a mathematics point of view

Goodmorning, I'm a university math student. I'm quiet familiar with differential geometry and I want to study the theory of general Relativity. I try to read some books, but all of these explain the ...
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1answer
40 views

What is the area under this graph? I am getting 2 different answers when using two different methods.

I found the area of the triangle using the formula first and got 2.25 Then found the area of the trapezium (Area of the whole graph) and subtracted the unshaded region and got 2.25 again. The third ...
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25 views

Heisenberg uncertainty principle in D-dimensional

For Heisenberg uncertainty principle in D-dimensional there is $d^2$ in the formula.where does this additional term comes compared with the case of one dimensional?
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0answers
41 views

how to transform a quadratic equation into a matrix form?

I have this type of equation: $$ - a^ {2} A - \eta ^{2} B - a \eta C - b^{2} A' - \eta' ^{2} B' - b \eta' C' - a \eta' D - b\eta E $$ The capital letters, $A, A', B, B', C, C', D, E$ are just the ...
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33 views

Root space of a Semi simple group an LVS?

A semi-simple Lie group has a Cartan Subalgebra ($H$) (CSA) -an LVS, Dual to this CSA LVS is root space($H^*$), which is set funtionals that map elements of CSA to real numbers and hence useful in ...
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1answer
18 views

definition of a smooth scalar potential

Have been asked to show that any flow described by a smooth scalar potential is irrotational. I know to show if a flow is irrotational curl of q = 0. But not too sure what is meant by smooth scalar ...
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1answer
30 views

A question about John Baez's definition of “stochastic Petri nets”.

John Baez, in his blog posts, introduces stochastic Petri nets as a Petri net that contains an additional function which maps each transition in the set of transitions $T$ to a real number. This ...
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0answers
45 views

Invalid use of the analytic continuation of the Riemann zeta function?

Watching this video on You Tube I got the impression that some sciences (in this case physics) use the analytic continuation of the Riemann zeta function without justification. Maybe this is just my ...
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40 views

Geodesic of symplectic manifold

Can I define geodesic on a manifold without Riemann structure? To be more specific, how can I define geodesic at symplectic manifold? Let's just look at simple case with symplectic form as ...
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1answer
111 views

Homotopy quantum field theories as functors

A homotopy quantum field theory is a symmetric monoidal functor $\tau:\mathrm{HCobord}(n,X)\to\mathrm{Vect}_{\mathbb{K}}$, with $X$ a path connected space with basepoint $\ast$. There is the following ...
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1answer
38 views

Solutions to differential equation

Let $\left\{a,\lambda\right\}\subset\mathbb{R}$. Let the following differential equation for a function $x\left(t\right)\in\mathbb{R}^{\mathbb{R}}$ be given: $$ \boxed ...
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2answers
43 views

Calculate velocity after certain displacement

Given is a function $a(t)$ for the acceleration. Starting from an initial velocity $v_0$ I want to calculate the velocity $v_1$ after a certain displacement $s$. Is this calculation possible since ...
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2answers
100 views

Studying maths for physicists [closed]

I am looking forward to be a theoretical physicist ,to unify general relativity and quantum mechanics ( to make the theory of everything ) How should I study maths? Should I study proofs of ...
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54 views

Decoupling system of two partial differential equations

If I have the following systems of PDE $$ u_t+x^2u_{xx}-\dfrac{h_1(t)}{h_0(t)}e^{-(v-u)}-\dfrac{h_0'(t)}{h_0(t)} = 0,\\ v_t-\dfrac{h_0(t)}{h_1(t)}e^{-(u-v)}-\dfrac{h_1'(t)}{h_1(t)} = 0, $$ where ...
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2answers
95 views

Sketching phase portraits [closed]

I am trying to answer this question: I would like to know how I go about drawing a phase portrait. All of the examples in my notes are simply the solution with no explanation, and this method of ...
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1answer
43 views

Changing variables for a partial differential equation

If I have the following systems of PDE \begin{align} u_t+x^2u_{xx}-\dfrac{h_1(t)}{h_0(t)}e^{-(v-u)}-\dfrac{h_0'(t)}{h_0(t)}=0\\ v_t-\dfrac{h_0(t)}{h_1(t)}e^{-(u-v)}-\dfrac{h_1'(t)}{h_1(t)}=0, ...
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1answer
49 views

Direct Delta Function

I was reading a Mathematics for Physics book when I saw these exercises. By using the knowledge of direct delta function, show that: $\int_{-\infty }^{+\infty }f(x)\delta '(x-y)dx=-f'(y)$ ...