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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.
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If it exists, can cross sections of a real tesseract appear to us in 3D space completely different than Schlegel diagram?
We as human beings cannot comprehend how an object looks like in spatial dimensions higher than 3, it is in fact unimaginable. Yet, in mathematics we are able to project analogues of objects from ... geometry mathematical-physics projective-geometry projective-space dimension-theory-analysis- 1
the deviation of the string from the equilibrium state is given by the function
I tried laplace but didn´t work. i don´t know how to start it physics mathematical-physics- 19
Period of Cartan 3-form
A Cartan 3-form in a Lie group $G$ is defined as: $$\omega = Tr(g^{-1}dg\wedge g^{-1}dg\wedge g^{-1}dg)$$ For $g$ being maps $g:B\longrightarrow G$, with $B$ a given manifold. The so-called periods of ... physics mathematical-physics string-theory cartan-geometry- 161
Primitive of a function of the form $\int \frac{21t}{21+t^2}\cdot \cos(bt)\; \mathrm{dt}$. I can't understand result obtained using python. [closed]
I tried to find primitive (indefinite integral) of a function of the form below. The function is of the form $$\int \frac{21t}{21+t^2}\cdot \cos(bt)\; \mathrm{dt}$$ Python gives the following result $$... integration mathematical-physics python- 19
Entropy increase in a finite set
A finite set M (playing the role of an energy shell $Γ_{mc}$) has $10^{100} − 1$ elements and is partitioned in $Γ_ν, ν = 1, . . . , 100$, with $\#Γ_ν = 0.9×10^ν$ . The “trajectory” (x(0), x(1), x(2), ... statistics physics mathematical-physics entropy statistical-mechanics- 49
Solve $\int_{-\infty}^\infty \frac{x}g \ln(1+gA^2 e^\frac{-(x-h)^2}{w^2})dx$ where $g,A,w,h$ are constants.
How to solve $\int_{-\infty}^\infty \frac{x}g \ln(1+gA^2 e^\frac{-(x-h)^2}{w^2})dx$ where $g,A,w,h$ are constants? integration mathematical-physics- 1
Combinatorial problem: triple binomial product related to squared Laguerre polynomials
Context Hydrogenic wavefunctions [1] include a factor given by Laguerre polynomials [2]. These wavefunctions are often encountered in a first course in quantum mechanics. They also appear in ... combinatorics binomial-coefficients special-functions mathematical-physics laguerre-polynomials- 793
Evaluate $\left(\frac{1}{2\cdot \pi}\right)\int_0^{[\pi]}15\cdot e^{-tni}dt+\int_\pi^{[2\pi]}0\cdot e^{-tni}dt$
Problem $$\left(\frac{1}{2\cdot \pi}\right)\int_0^{[\pi]}15\cdot e^{-tni}dt+\int_\pi^{[2\pi]}0\cdot e^{-tni}dt$$ When I manually solve this question, I get this result $$\frac{j15}{2n\pi}(\cos n\pi-... calculus integration complex-analysis complex-numbers mathematical-physics- 11
Covariant derivative on associated vector bundle under change of section
Let $(P,\pi,M;G)$ be a principal bundle with connection form $A\in\mathcal{C}(P)$ and let $\rho:G\rightarrow\mathrm{GL}(V)$ be a representation of $G$ on some finite-dimensional vector space $V$. From ... differential-geometry mathematical-physics connections- 391
Does fundamental theorem of calculus apply to closed curves? If yes why the closed line integral of a function is not zero?
Why closed curve integral $$\oint A.dl$$ doesn't give us zero in many physics related examples? Closed line/loop/curve/contour have same starting and end points and according to fundamental theorem ... complex-analysis multivariable-calculus vector-analysis mathematical-physics curl- 1
Equivalence of reaction-diffusion
For $N$ cells in a one-dimensional ring, imagine a dynamical system given by, for each cell $1\leq i\leq N$ $$ \begin{align} \frac{dx_i}{dt}&=f(x_i,y_{i-1},y_{i+1})\\ \frac{dy_i}{dt}&=g(x_i,y_{... ordinary-differential-equations partial-differential-equations dynamical-systems physics mathematical-physics- 3,418
Defining Fourier Transform on an $L^{2}$ space
Suppose we have a square $[-\frac{L}{2},\frac{L}{2}]^{N}$ on $\mathbb{R}^{N}$ for some $L>1$ and take $S$ to be a finite and discrete set. Here I will take $S = \{-1,1\}$. Consider the space $L^{2}\... analysis fourier-analysis fourier-transform mathematical-physics- 1,453
How do I calculate the covarient derivative of a type (2,1) or (1,2) tensor
The following tensor I need help calculating the covarient derivative are as follows: and I know the general rule when it comes to a type (0,2) tensor is and I know the general rule when it comes ... physics mathematical-physics- 11
Further question on an existing question about: The Newtonian Central Force System
Still on the question: Understanding shift to polar coordinates in the newtonian central force system of ODE's The book states that $\dfrac{X}{|X|^{3}} = -\dfrac{1}{r^{2}} (\text{cos}(\theta),\... ordinary-differential-equations dynamical-systems mathematical-physics- 511
Fourier transform of rectangular pulse
Calculate the Fourier transform of rectangular pulse given below. (Height, A; width, 2a) . I tried to calculate that but I am not sure whether it s correct or not. Question Answer fourier-series mathematical-physics- 1
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