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Questions tagged [mathematical-physics]

DO NOT USE THIS TAG for elementary physical questions. This tag is intended for questions on modern mathematical methods used in quantum theory, general relativity, string theory, integrable system etc at an advanced undergraduate or graduate level.

"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 mathematical methods used in quantum theory, general relativity, string theory, integrable system etc at an advanced undergraduate or graduate level.

Do not use just because your question involves physics!

See also Physics Stack Exchange's discussion on mathematical physics, Math Overflow's discussion on mathematical physics and Physics Overflow for further reference.

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Bessel, Hankel, Legendre

I was asking myself... What relationship is there,what have they in common Bessel, Hankel and Legendre functions?..in terms of Helmholtz equations.
alb084
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Divergence of series

I wanted to test the convergence of $1/n^{ln3}$ as n tends to infinity. I applied the integral test and found that the integral is (ln n) which certainly diverges as n tends to infinity. But the answer given is that this given series is…
Md Kashif
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Why will this object never stop?

Suppose an object is initially at x = 0 and at rest. It is then acted on by a force F which depends on it’s position as follows $$ F(x) = +\frac{1}{1+x^2} $$ Without any other forces acting argue why the object never stops. Also, how much energy…
Dank memer
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What does this relation signify?

I recently came across this in social media- What doe the last equation mean?Is it somehow connected to probability or something? Thanks a lot for any help or response!!
Soham
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Collision of massive black holes at the speed of light

The time slows down due to two reasons: $1.$ high speed, $2.$ high mass relative to the radius. Basically, assuming that we are living on a black hole, we will very very slowly get older compared to the others. On the other hand if we travel at near…
Seyhmus Güngören
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Calculating acceleration of a body

I have the question "A body moves in a circle with a radius 450 km. The velocity at a point in the circle is 16 ms^-1. What is the acceleration of the body towards the circle at this point?" So I know that the radius is 450000 metres and the…
Dan
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Calculating total energy

I have the question: "Calculate the total energy of the moving object, when mass = $4$ kg, acceleration due to gravity = $9.81~\text{ms}^{-2}$, height = $10$ m and velocity = $3~\text{ms}^{-1}$" I know that Total energy = potential energy +…
Dan
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logical reasoning problem

A man starts a journey by driving directly South for 30 km, then directly East for 40 km, and finally directly North for 60 km. What is the shortest distance between the points where he stopped and where he started? Pls help!
Hana
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Why is this operator self-adjoint (or is it)?

I am reading literature on self-adjoint extensions of Hamiltonians (particle interaction) and I came across the following statement (in context of separating total momentum $P$): Operator $H$ defined by $(Hf)(P)=\frac{P^2}{m+2}f(P)$ is a …
nakajuice
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What's the value of $\int f(x)\delta(x-a) dx$ if $a$ is not in the domain of integration?

A problem occurs when I was solving an exersice of perturbative kind. The delta function has the fundamental property that \begin{align} \int_{-\infty}^{\infty}f(x)\delta(x-a)dx=f(a) \end{align} and, in…
aaa
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Hamiltonian mechanics: constant energy hypersurfaces with $dH \neq 0$

I read substantially the following sentence in Frankel's "Geometry of physics": Look now at the level set $$V_{E}=\left\{(p,q)\in T^{*}M:H(p,q)=E\right\}$$ where $T^{*}M$ is the cotangent space, $p$ and $q$ respectively the momenta and the…
Slz2718
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Static Friction

The coefficient of static friction between car’s tires and a level road is 0.80. If the car is to be stopped in a maximum time of 3.0 s, its maximum speed is (a) 2.4 m/s (b) 23.5 m/s (c) 7.8 m/s (d) 2.6…
Bok
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Right Propagating Wave complex

Does it make sense to think of $e^{ikx}\equiv $cos$(kx)+i$sin$(kx)$ as a right propagating wave? I am rather confused by the imaginary term here. Context: \begin{equation} \phi(x)=\begin{cases} Ae^{ik_1x}+Be^{-ik_1x}, & \text{if $x<0$}.\\ …
usainlightning
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Toppling of a road cone that has an axis at an angle $\alpha$ to the horizontal.

A road cone consists of a $45cm$ x $45cm$ square base of height $10cm$, and a conical shell of radius $15cm$ and height $75cm$. The base has a circular hole through it , of radius $15cm$, to aid stacking. The base is made of plastic of density $1Kg$…
J132
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Calorimetry Question

If you are familiar with the formula q = (m) * (c) * (Delta Temperature) q = (Delta Heat) m = Mass c = Heat Capacity Delta T = Change in temperature The question is asking to solve with this info: The heat capacity is 440 KJ/Degrees Celcius. The…
Imagine Dragons
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