# Tagged Questions

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### Applications of Algebra in Physics

Often I have heard about the link between Algebra (in particular Representations of Groups and Algebras) and some "indefinite" field of Physics. I have a good preparation in Algebra and ...
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### Basis representation for non-negative, compact support, reasonably smooth spectral function

I was wondering if anyone has ideas on representing a non-negative, compact support (from x=-1 to 1 on the real axis) spectral function as a superposition of basis elements. Ideally, the basis ...
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### Can a quaternionic Kähler manifold be NOT Kähler?

I have an explicit construction of the metric on the quaternionic Kähler manifold $$\mathcal M = \frac{Sp(1, 1)}{Sp(1) \times Sp(1)}.$$ Arranging the four real degrees of freedom into two complex ones ...
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### Properties of functional integration

this question comes from theoretical Physics, the issue being the so called Path Integral. The measure of this thing is something written as $[d\phi]=\prod_x d\phi(x)$ And this should be the limit ...
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### derivation of an equation involving the Fourier transform of the square modulus of a wave function

A textbook on electron optics states that, ignoring a factor of 2 for convenience, the result $\mathscr{F}(I(\vec{r}))=\mathscr{F}(\phi(\vec{r}))\cdot{}A(\vec{k})\cdot{}\sin[\gamma(\vec{k})]$ can be ...
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### integral of the sphere describing lambertian reflectance

A Lambertian surface reflects or emits radiation proportional to the cosine of the angle subtended between the exiting angle and the normal to that surface. The integral of surface of the hemisphere ...
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### Formulation VS Interpretation

I'm reading a book on Mathematical Physics and at some point the author says that we must distinguish between a "formulation" and an "interpretation" of a theory, although it's not easy to point what ...
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### Resources for learning Relativity

I´m looking for books to the study of Relativity. I know that this is math stack schange and not physics stack schage, but I believe that some of the users here are interesed in physical-mathematical ...
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### Centre of Mass and Moment of Inertia of a sphere - spherical cap

I have been given a sphere of radius a, from this sphere a cap of hight h is cut off. 1) What is the centre of mass of the rest of the sphere? 2) What is the moment of inertia regarding the axis of ...
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### is it necessary that curl of 2d vector is perpendicular to the plane.

I am just confused, help me guys. The question comes up, because we say that curl is either clockwise or anti-clockwise at a point.
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### If physical space had cardinality larger than $\aleph_1$, would we need new math to describe dynamics? [closed]

If physical space had cardinality larger than $\aleph_1$, would we need new math to describe dynamics? For instance, would the dynamics of a sea of virtual particles of cardinality $\aleph_1$ would ...
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### Collision detection between two accelerating spheres with no initial velocity?

We have two non-touching spheres of radii r1 & r2 are lying in space at rest. Both of them are then given accelerations a1 & a2 respectively at time t=0. Find whether they will ever come in ...
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### Mathematics/Mechanics Problem

I would like to ask you if anybody could help me with this problem. So far i know that the positions where B and A have to meet are at distances L and L+2r
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consider the following situation of a double pendulum. We found the moving equations as $$\ddot{\theta_1}=-L_1\sin\theta_1 + \frac{m_2}{m_1}\cos\theta_2\sin(\theta_2-\theta_1),\\ ... 0answers 37 views ### Why is the space of trajectories for a particle a cotangent bundle? In Paugams book, Towards the Mathematics of Quantum Field Theory, he writes the following in the introduction: Let us first illustrate this very general notion by the simple example of Newtonian ... 0answers 74 views ### Are there any legitimate examples of applications of set theory to Physics? Sets are of course ubiquitous, so in this sense set theory is applicable to physics. But I'm thinking more like techniques like forcing, or constructs like cardinals or ordinals. Intuitively it ... 1answer 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 ... 4answers 71 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 ... 1answer 27 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 ... 0answers 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 ... 0answers 25 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 ... 0answers 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 ... 1answer 56 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 ... 1answer 59 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 ... 0answers 22 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 ... 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 ... 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 ... 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 ... 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 ... 0answers 49 views ### Clarification on some notation and “assumptions” in page 143-144 of the book “Quantum Fields and Strings: A Course for Mathematicians, Volume 1” I was trying to read the chapter 1 (at page 143) of this book Quantum Fields and Strings: A Course for Mathematicians, Volume 1 that is supposed to be an introduction to modern quantum field ... 1answer 78 views ### How can the tension force be computed to test if a shape is moving or not? Source Given the coordinates of n 3D joints (1kg each) connected by m rods. Assume rods have zero mass and joints with z=0 are fixed to the ground while others are free to move, will the shape be ... 2answers 109 views ### A problem about symplectic manifolds in Arnold's book There is a problem in Arnold's Mathematical Methods of Classical Mechanics which says that: Show that the map A: \mathbb{R}^{2n} \rightarrow \mathbb{R}^{2n} sending (p, q) \rightarrow (P(p,q), ... 1answer 72 views ### How to compute force on joints of a 3D structure of balls connected by rods? Source Given the coordinates of n 3D joints (1kg each) connected by m rods. Assume rods have zero mass and joints with z=0 are fixed to the ground while others are free to move, will the shape be ... 0answers 36 views ### C. Neumann passage in Latin from *Annali di Matematica Pura ed Applicata* Neumann, Carl. “Theoria nova phaenomenis electricis applicanda.” Annali di Matematica Pura ed Applicata 2, no. 1 (August 1868): 120–128. doi:10.1007/BF02419606. p. 121: Nova introducitur ... 1answer 35 views ### Explanation on equations please [closed] I've got seemingly two different equations for velocity in orbit:$$v_1 = \sqrt{ \frac{2GM}{R}} $$and$$v = \sqrt{ \frac{Gm_e}{R}}$$What is the difference between these two? I'm quite sure that ... 1answer 19 views ### When finding the frequencies of normal modes, can you have a negative frequency? Do you simply just consider the positive solutions? I tried a google search but didn't find anything quickly. The work I am studying is Lagrangian systems. 0answers 32 views ### Shooting a grenade - angle throwing In my 3D simulation/game I need to shoot a grenade from a grenade launcher. The movement of the grenade is already setup by someone else. all I need is to give him the pitch angle of the grenade ... 0answers 28 views ### Solution to the “cubic” Helmholtz equation What is known about the solutions of the differential equation in three-dimensions$$ \nabla^2 \phi = -\kappa^2 (\phi + (1/3!)\phi^3) $$Without the cubic term, this gives a linear operator ... 0answers 40 views ### Finding angular momentum about the center of mass? If we have a couple of particles of an equal, unknown mass: r_{+} = (c + e^{-Bt} \cos({\theta}))\textbf{x} + (d + e^{-Bt} \sin({\theta}))\textbf{y} r_{-} = (c - e^{-Bt} \cos({\theta}))\textbf{x} ... 1answer 63 views ### Solve without convergance? Two days ago I recalled a problem I was given a long time ago. The problem is: Four ants are placed on the vertices of a square with side 1. The ants start moving, each directed towards its left ... 1answer 18 views ### How to work out 3 dimensional vector angles I've come across this question and cant for the life of me think how to work it out. I understand working out the angle between two vectors e.g. given, vector a(2i+3j-k) and vector b(8i-6j+2k) but am ... 5answers 543 views ### What physics book for aspiring theoretical physicist / pure mathematician [closed] I am a high school student. I want to learn physics on my own, but I am puzzled : Should I read a book which talks about all branches of physics? If yes, recommend a book. Should I read a book which ... 0answers 24 views ### a group of order 32 Consider the creation and annihilation operators \left\{a_{1},a_{2},b_{1},b_{2}\right\}:$$[a_{i},a_{j}]_{+}=0,[b_{i},b_{j}]_{+}=0, a_{i},b_{j}]_{+}=\delta^{j}_{i} with ...
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 ...