"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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Mathematics needed in the study of Quantum Physics

As a 12th grade student , I'm currently acquainted with single variable calculus, algebra, and geometry, obviously on a high school level. I tried taking a Quantum Physics course on coursera.com, but ...
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1answer
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The Gaussian Integral

Hi I am trying to calculate the expected value of $$ \mathbb{E}\big[x_i x_j...x_N\big]=\int_{-\infty}^\infty x_ix_jx_k...x_N \exp\bigg({-\sum_{i,j=1}^N\frac{1}{2}x^\top_i A_{ij}x_j}-\sum_{i=1}^Nh_i ...
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How to do This Torque problem? [on hold]

The answer for the Question is 0.15kg. Is there any problem with the question because I cant seem to solve it. You can try working backwards.
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1answer
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Wronskian Bessel Equations

I need to compute the wronskian of $J_n$ and $Y_n$ (the Bessel functions of the first and second kinds). I've been able to find in many sources that it is $$W(J_n,Y_n)=\frac{\pi}{2x}$$, but I haven't ...
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0answers
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Complex Number Plane Physics Math Problem

Show that if the line through the origin and the point z is rotated 90°about the origin, it becomes the line through the origin and the point iz. Use this idea in the following problem: Let ...
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0answers
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Euler Bernoulli beam

A simple model of the beam subjected to bending stresses is given by Euler-Bernoulli differential equation. Finite element discretization leads to a system of liniar equations.As discretization size ...
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2answers
15 views

How can you determine Mass / kg from the attached table

I spent the last two hours trying to figure out part D and I can't get my head around it... Part D has the formula mass/kg = Mass/kg = C / ΣC I'd imagine "C" is the number of C section of the ...
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0answers
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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 ...
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0answers
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Free lecture notes to Carl Bender's Mathematical Physics video lecture course?

I am just watching Carl Bender's Mathematical Physics video lecture course (about asymptotics and its application in physics) http://www.perimeterscholars.org/328.html which is great! Are there any ...
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Linearize a specific eqution

Is it possible to linearize this equation ? I tried without success .. ...
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2answers
36 views

Trace in non-orthogonal basis

In Dirac notation we can define the trace of an operator in Hilbert space $\rho$ as the follows, $Tr(\rho)=\sum\limits_{|s\rangle \in B} \langle s| \rho |s\rangle$ where B is some orthonormal ...
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0answers
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Determining how accurate an ellipse fit is

So I have an image of bacteria particles which are often shaped very irregularly with many grooves. Im trying to fit ellipses onto these particles so I can get a better, more smooth analysis of the ...
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1answer
68 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 ...
3
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2answers
89 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), ...
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1answer
45 views

Representation theory and particle physics

Are there good books which explain clearly explain the connections between modern particle physics and representation theory of groups and lie algebras?
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26 views

Integral-Differential Equation Modeling Banked Turn

Solve this equation for the function $y(x)$: $y' = \alpha \left(\int\sqrt{1 + y'^2} dx \right)^2$ Of course this must first be solved for $y'$ and then integrated to get $y$. The following is not ...
3
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1answer
50 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 ...
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1answer
25 views

How many gallons are used in the U.S. each day and if this gasoline were used to fill a cubical tank how big would one side be?

The question I am trying to solve is: Part I) How many gallons of gasoline are used in the U.S. in one day assuming there are $2$ cars for every $3$ people and each car is driven $10,000$ miles a ...
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0answers
16 views

Force to change the base length of an isosceles triangle

Given an isosceles triangle with legs 7' long weighing 160lbs. What horizontal force would be required to change the base width from 15' to 13'? The ends are on wheels-so assume perfect conditions ...
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0answers
31 views

How long does it take for a vehicle to go from 0 to 60 mph?

I found the freefall motion equation which describes terminal velocity of a falling body, but I can't find a similar equation for a vehicle subject to constant traction force, so I tried determining ...
3
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2answers
103 views

Integral $\int_0^\infty e^{imx^2}dx$

In evaluating an integral in path integrals in QFT, I am stuck with this integral (that came up from evaluating a functional integral), $$I = \bigg( \frac{m}{2\pi i\tau}\bigg) \int ...
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0answers
13 views

How could a vector field fluctuate?

Reynolds decomposition of velocity vector field into two time average and fluctuating parts. how could a vector field fluctuate?
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0answers
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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 ...
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1answer
11 views

Deriving relative position from instanteous acceleration and time

I'm working on a mobile app that uses the accelerometer to move a cursor. Although it's technically a computer science problem, once you get past how you get the values, it's more of a math problem, ...
0
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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 ...
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1answer
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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.
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0answers
23 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 ...
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0answers
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Converse of Noether's (first) theorem

Noether's (first) theorem states that if a Lagrangian $L$ admits a continuous symmetry, then the following quantity are conserved. $$\left(\frac{\partial L}{\partial \dot q}\cdot\dot ...
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3answers
35 views

Planet Simulation Newtons Law - Downscaling

I would like to scale-down the original numbers of our planet's motion, as i cannot properly visualize it in Unity3D (Game-Engine). I have: 1) Initial Position (-3.5e10, 0) (km) 2) Initial ...
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0answers
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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 ...
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0answers
38 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} ...
2
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1answer
59 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 ...
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1answer
30 views

Non-invertible operators

Can the matrix representation of some linear operators on some vector space be singular?
0
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1answer
47 views

Vector Space of Lie Algebra

Lie algebra $ \mathfrak{g} $ for a Lie group $ \mathcal{G}$ is closed under commutation. Also, the elements of Lie Algebra form a Linear Vector Space(LVS). Firstly, when is it allowed to define an ...
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2answers
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Integral calculus question relating to particle motion

"A particle of mass m is attracted toward a fixed point 0 with a force inversely proportional to its instantaneous distance from 0. If the particle is released from rest, at distance L, from 0, find ...
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1answer
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Implicit Partial derivative computation for 3rd order Runge Kutta derivation?

I need to derive the 3rd order Runge Kutta method which needs a tedious computation of partial derivatives, which i have a feeling i will make a mistake on eventually. I was wondering if there is any ...
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1answer
38 views

A question to clarify the use of divergent series in calculating the casimir effect

I asked this question already on both Physics SE and quora, but I did not get an answer on either of these Q&A venues. I know this is strictly speaking not a mathematics question, but could the ...
3
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1answer
45 views

Connection(gauge field) in Fubini-Study metric is pull back of a connection A of line bundle $\mathcal{O}(1)$ on $\mathbb{CP}^{N-1}$

One can describe a $\mathbb{CP}^{N-1}$ manifold with a Fubini-Study metric $g^{FS}$, and there is a connection one form $v$ on it. A is connection one form(gauge field) of a line ...
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0answers
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Short examples that are/are not quantum-ergodic

Are there any considerably short examples of manifolds that are/aren't quantum ergodic, or quantum unique ergodic? Note that a (compact) Riemannian manifold is said to be quantum ergodic if ...
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0answers
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What methods are available for this optimization problem?

I have an intermediate knowledge of the calculus of variations: I can handle constraints in functional or integral forms and extrapolate to multiple variables and functions. If I dig in my notebooks I ...
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1answer
15 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 ...
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5answers
455 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 ...
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1answer
12 views

we need to find unit vector along the reflected ray.

A ray of light on a plane mirror comes along a vector $i+j-k$ The normal on incidence point is along $i+j$ we need to find unit vector along the reflected ray. I am not able to solve and draw the ...
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2answers
69 views

Is it possible to mathematically explain why solids go under mollification when heated?

Well, I'm sure that many people on MSE might object that this is not a math question, however, I think that there might be a well-posed mathematical answer to this question, or at least I hope so. We ...
2
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1answer
96 views

Can you prove $F=ma$ mathematically?

So, it is one of Hilbert's famous problems to "axiomatize physics". In these attempts to establish physics as a subfield of mathematics, I wonder where does the Newton's law $F=ma$ stand. To be ...
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1answer
34 views

Integration involving multiple constants…

So I've been tackling the rather nasty integral of... $\int^R_s\frac{2r}{\sqrt{r^2-s^2}}.\frac{1}{2}(R-r)^2dr$ ...where R and s are constants. However, every method I try I seem to get stumped by ...
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0answers
55 views

What is the reason that Veneziano uses Euler's beta function?

This is veneziano amplitude: $$B(-a(s),-a(t))$$ where the $a(s)$ and $a(t)$ are a kind of leading trajectories (regge trajectory). which is born of strings theory. What is the reason that Euler's ...
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0answers
15 views

Is mathematical formulation of Quantum electrodynamics applicable to Quantum gravitodynamics (QGD), through Estakhr's Elementary Gravitational Mass?

Consider Estakhr analogy between elementary electric charge and elementary gravitational mass constants. $$e=q_p\sqrt{a_e}$$, where $e$ denotes elementary charge, $q_p$ planck's charge, $a_e$ fine ...
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1answer
32 views

Can asymptotic series include negative exponents (Laurent series)?

An series $\{a_n\}$ to a function $f(x)$ is defined as $$ f(x) - \sum\limits_{n=0}^{N} a_n x^n\sim a_{N+1}x^{N+1} $$ as $x \rightarrow x_0$ for all N. I have just heard, that the exponents $n$ do ...
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2answers
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Question about Bernoulli Distribution calculation

can sombody explain the above calculation in the red circle marked with "why?"? I am studying MLE with Bernoulli Distribution, and in the middle of a video clip, the lecturer says $ 1\over{n} ...