Questions related to mathematical physics which include application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories

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3
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2answers
156 views

Gödel's incompleteness theorems

In the last paragraph of Stephan Hawking's speech "Godel and the End of the Universe", he mentioned "... I'm now glad that our search for understanding will never come to an end, and that we will ...
0
votes
0answers
37 views

Subject to in equation

I have the formula below: $$\hat x_2=\arg\min\lVert x\rVert_2\quad\text{subject to}\quad A{x}=y.$$ But I didn't understand what was meant by "subject to" ? does $x$ is replaced by $x_2$? please can ...
13
votes
5answers
824 views

In what ways has physics spurred the invention of new mathematical tools?

I came across this comment: Mathematical rigor is not a criterion that physicists have for evaluating their theories. From a mathematical perspective, the non-rigorous theories are far more ...
0
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1answer
101 views

Help with polar coordinates for physics problem

I need to solve a physics problem but don't know about polar coordinates properly, can anybody help with it? Suppose a curve which is a current carrying wire: $$r=\frac ...
1
vote
1answer
42 views

Why can we make this integral change of limits? Is it obvious?

When deriving the equation for the impulse-momentum theorem, the following occurs: $$\cdots=\int\limits_{t_1}^{t_2}\frac{d\vec p}{dt}dt = \int\limits_{\vec p_1}^{\vec p_2}d\vec p=\cdots$$ I know the ...
1
vote
3answers
102 views

Books that integrate physical reasoning with mathematical reasoning? mathematicians?

As the title says, can anyone help me to find any book that shows how physical reasoning using concepts from classical/quantum mechanics and physics in general can enlighten us about mathematical ...
10
votes
2answers
189 views

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 ...
4
votes
0answers
45 views

How to integrate scalar field over quarter torus? Infinite series does not converge.

This seems to be physics question, but the problem just concerns math. Preface If one wants to calculate the permeance $P$ of a rectangular bar: it is an easy task: $$P = \frac{\mu a b}{L} ...
0
votes
0answers
49 views

Derivative with respect to a vector and tensor on a manifold

I am reading through a paper and have come across a statement which I do not fully understand. I paraphrase below. Consider a scalar function $f = ...
0
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1answer
43 views

How to show $\psi^*(x,-t)$ is also solution of the Schrodinger equation

I've seen it stated that it "can easily be seen" that if $\psi(r,t)$ is a solution of the Schrodinger equation : $ih \dfrac{\partial \psi(r,t)}{\partial t} = H \psi(r,t)$, then $\psi^*(r,-t)$ is also ...
1
vote
0answers
30 views

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 ...
2
votes
0answers
47 views

Calculating work [closed]

How much work is required to lift a $1000\mathrm{kg}$ satellite from the surface of the earth to an altitude of $2\times10^6$ meters? The gravitational force is $F=\frac{GMm}{r^2}$, where $M$ is the ...
2
votes
1answer
80 views

Solving weak 2 body problem

I tried to solve a physics problem about two body problem where the masses $M$ and $m$ are $M \gg m$. The body $m$ is at radius $R$ from the mass $M$ and is falling down with initial speed $v(0) = 0$. ...
0
votes
1answer
51 views

Are distance-related paradoxes limited by the size of an atom?

See these 2 paradoxes: Coastline paradox The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. ...
2
votes
0answers
35 views

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 ...
0
votes
0answers
31 views

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 ...
0
votes
0answers
23 views

Stopping angular momentum to obtain a particular angle

While the overall project relates to software development, it boils down to a simple (i think) physics problem. I have a joint (a motor, pretty much.) that needs to move to a specific angle. I can ...
0
votes
3answers
70 views

Maxwell's Equations Divergence Question

$$ \left\{ \begin{align} \text{div } \textbf{E} & =0, \\ \text{div } \textbf{H} & =0, \\ \text{curl } \textbf{E} & = \frac{-1}{c} \frac{\partial \textbf{H}}{\partial t}, \\ \text{curl } ...
0
votes
1answer
51 views

Maxwell's Equations Curl Question

$$\left\{ \begin{align} \text{div } \textbf{E} &=0, \\ \text{div } \textbf{H} & =0, \\ \text{curl } \textbf{E} & = \dfrac{-1}{c} \dfrac{\partial\textbf{H}}{\partial t}, \\\text{curl } ...
0
votes
1answer
38 views

Triangulation in delayed loudspeaker setup

I could use some help with the following situation. Two physically displaced speakers need to arrive on time, in order to achieve summation, for a given position (green dot) within a listening plane ...
1
vote
2answers
37 views

Calculating appearance of size of object at given distance

Here's the problem I'd like to solve. If I'm 1 ft away from a computer screen and a word on the screen appears a certain size, is there an equation or calculation that will tell me how big that ...
2
votes
0answers
78 views

Why is Grassman integration so weird?

Why are Grassman integration and differentiation equivalent? The only justification of this definition I have ever scene is "Well, how else could it work?" Indeed, I don't have any other suggestions, ...
2
votes
1answer
32 views

differential in integration cancelled but variable endpoint is changed

In kinetic energy equation in wiki. I have difficulty problem how endpoint in integral change from t to v. This doesn't look like it is using substitution method. ...
0
votes
0answers
53 views

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 ...
0
votes
0answers
35 views

Where are the time dilatational effects of orbital motion and gravitational acceleration equal?

This might not be the right forum to ask this question, but it is very interesting. Nearly four years ago, upon hearing of the observation of time dilation in two optical atomic clocks at an ...
1
vote
3answers
69 views

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 ...
2
votes
0answers
54 views

ODE particular solution (physics)

I have to do this exercise: ($Z(t)=I(t)$, it's printed wrong). I have a doubt about the first item. To find all resonance when $R=1$, I found the particular solution $I_{p}(t)=A\sin(\omega ...
0
votes
0answers
72 views

Angular displacement/speed of a rotating sphere from 3d points

I have 3d points on the surface of a unit sphere that describe every minute its rotation. I want to know angular velocity of this sphere. The sphere center is fixed and the axis of rotation can change ...
1
vote
1answer
344 views

Word Problem, Calculus estimation homework

Roger runs a marathon. His friend Jeff rides behind him on a bicycle and clocks his speed every 15 minutes. Roger starts out strong, but after an hour and a half he is so exhausted that he has to ...
0
votes
1answer
65 views

Partitions applications in physics

Is there any direct application of all developments related to partitions? I am specially interested in physics but cryptography or other mostly theoretical areas would also be a good answer. By ...
5
votes
2answers
167 views

Solution of differential equation with Dirac Delta

Is it possible to solve a differential equation of the following form? $\partial_x^2y + \delta(x) \partial_x y = 0$ where $\delta(x)$ is the dirac delta function. I need the solution for periodic ...
1
vote
1answer
44 views

How to properly generalize a definite integral?

I know, I know. On the can, this problem seems simple. Just take $\int_a^bf(x)\mathrm{d}x$ and write is as $\int f(x)\mathrm{d}x$. However, when I tried to do that on an Engineering Dynamics ...
0
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3answers
52 views

Rate of change question (planes, kites and the such)

Q: A kite $100 \ m$ above the ground moves horizontally at a speed of $8 \ m/s$. At what rate is the angle between the string and the horizontal, i.e. e the ground, decreasing when $200 \ m$ of string ...
1
vote
1answer
66 views

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 ...
1
vote
1answer
81 views

Why does this get the angle of the surface?

I have this (physics) question, but am missing something as to why the math works for it. The problem is as follows: A 4- kg sphere rests on t he smooth parabolic surface. Determine the normal ...
2
votes
1answer
72 views

How we apply representation theory to physics.

I want to have a concrete idea of what people do with representation theory in physics. Here is what I think: Corresponding to a specific "physics", there is particularly a Lie group (called G) of ...
0
votes
0answers
26 views

Inter-neighbor resistance on triangular prism

Given a triangular prism of infinite length along the X direction. A graph is formed with the set of nodes all the points on an edge of the prism with integer values of X, and the with each node ...
3
votes
3answers
75 views

Representation theory in physics

0 down vote favorite I'm sorry if this is somewhat a dumb question. First: "Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements ...
0
votes
1answer
32 views

How far will my car roll given a function representing the slope of the landscape I'm driving on?

So I was driving in my car thinking to myself "I wonder how far I would go (before starting to roll backwards) if I just took my foot off the brakes" I tried to figure it out myself but could not. SO ...
0
votes
1answer
55 views

Why do these acceleration computations contradict each other?

A rocket follows the path $(y-40)^2=160x$ after traveling vertically to the height of 40 feet (making for a very convenient continuity. The problem asks "If the component velocity in the vertical ...
0
votes
1answer
29 views

Calculating the force on each of two directions needed to move object to destination

Given the following: How would you calculate the forces needed on the v and u directions to move point ...
2
votes
2answers
49 views

Differentiation of function

There is a passage in a physics textbook I don't quite follow. Since my question is mathematical, I've decided to post it here. The book says: Let $V$ be the volume of a molecule and assume $V = ...
1
vote
1answer
21 views

Evolution curves on dynamic system

The matrix of a linear dynamic system is: [0, 3] [3, 0] FACT: If A is the evolution curve that passes on point (1,1) in phase space and B the evolution curve that passes on point (1,-1) we can ...
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vote
0answers
69 views

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 ...
0
votes
3answers
193 views

Is speed a function of position?

Let $x$ be a smooth function from $[0,\infty)$ to $\mathbb{R}^n$ satisfying the following differential equation $x''(t) = f(x(t))$, where $f$ is a smooth function from $\mathbb{R}^n$ to itself. Then ...
0
votes
1answer
61 views

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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2answers
234 views

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.
1
vote
1answer
79 views

How to prove that something is finite

I'm given a physical model of something. Say it's a radius of a planet: $$R=\pi\left(\frac{n}{2\pi G}\right)^{1/2}$$ where $G$ is the universal gravitational constant, n - "positive constant" If I ...
2
votes
3answers
61 views

Minimum speed using calculus

I've been trying to answer this question , specifically part c) I've done part a) and b) where $U = \frac{28\sqrt{15}}{15} $ and $ \theta = 53.3 $ degrees . For the last part I need to work out the ...
2
votes
0answers
116 views

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 ...