Mathematics Stack Exchange
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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.

4085 questions
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Solution to y*ln(y)=x*exp(x)

Can anyone please help me with a close-form explicit solution to $y\times\ln(y)=x\times\exp(x)$ ? Please note that $y=\exp(x)$ is not the answer I am looking for. The equation actually looks like this $y=\exp(x/y*\exp(x))$
Song Li
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Simple introduction to the Replica Method: averaging the random partition function

I'm reading the paragraph 2.3 about the Replica Method and I fail to see how the first 3 formulas are derived one from another. Given the definition of $$ f = - \frac 1 {\beta N} \mathbb E \ln Z$$ and using the identity $$ \lim_ {n \to 0} \frac {Z^n…
Giulio
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Permutations with fixed number of distinct elements

This is a math question. I have been stumped to come up with a general formula for the following seemingly simple question. Given a number of distinct elements to choose from and choosing N, how many permutations exist that have a set number of…
alian
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Redundant term in Galilean transformation of time-dependent Schrödinger Equation

In my quantum physics book (Quantum Mechanincs Second edition B.H. Bransden & C.J. Joachain) in a chapter of Galilean transformation and Schrödinger equation there is a couple of weird equations. Let $\vec r, \vec u , \vec v \, \in \mathbb R^3$ and…
ludz
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How can I evaluate the material derivative of $\frac{\|\vec{v}\|^2}{2}$?

How can I evaluate the material derivative of $\frac{\|\vec{v}\|^2}{2}$ ? This question arises from the transport of the kinematic energy of a fluid: $$\frac{d}{dt}\int_{B_t} \rho \frac{\|\vec{v}\|^2}{2}\ dV = \int_{B_t} \rho \dot{\left(…
Gabrielek
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Center of mass of points in log scale chart

I would like to know what is the way to find the center of mass of some scattered points in a 2D plane where scales are logarithmic? Is it safe to first convert them to normal scale and then compute X_mean and Y_mean and then convert that to log…
mahmood
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Time taken for a floor to reach the ground

So the question is as follows: A building has $s$ floors each of height $h$. An explosion destroys the strength of the $n^{th}$ floor. You may assume that the building remains intact above the floor that explodes and that the momentum is conserved…
Bhavish Raghoo
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Computer Graphics Question

I'm learning computer graphics, but there are still some problem i really confuse and have nothing to do, maybe i'm still a beginner or maybe it hard, but, i really willing to learn these things, please help, problem is: The winding number of a…
Lê Quốc Khánh
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Shape of the common catenary

I have recently started studying Common Catenary (rope with uniform mass hanging between two points not on the same vertical line) . While deriving the equation of the common catenary , we assume that the bottom most part of the string is perfectly…
llecxe
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How do I write an equation that depicts an object scaling down towards zero?

Please pardon my lack of proper etiquette here on this platform. I'm trying to articulate an equation, perhaps a vector, that expresses an object that's scaling down towards zero. For example. In the movie "Honey I Shrunk the Kids". The kids were…
Tivity
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Is there a math relation between blurriness and eye power?

In computers science, the main idea behind blurring a photo is to set the RGB value of every pixel to the average of all the values of its neighbours. For more details on what I mean by "blur": Basic Concept More in detail I'm wondering if there is…
Tilak Madichetti
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Bessel functions, zeros, and frequencies

How can we find the first three zeros $k_{mn}$ of each of the Bessel functions J0, J1, J2, and J3. And how to find the first 6 frequencies of a vibrating circular membrane? So, I was thinking maybe Wolfram alpha, but need some clarification. thanks
Buddy Holly
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How to extend the first postulate of statistical thermodynamics to reach Gibbs postulate?

Question I'm searching for the derivation which enables me to say: The first postulate of statistical thermodynamics can be extended to arrive at the Gibbs postulate, a postulate which relates the energy of said microstates to internal energy…
More Anonymous
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Calculating net ventilation

I have the question: Here is my attempt is this correct ?
Dan
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Three-Body problem - Newtonian space

How to make formulation of the three-body problem if we suppose that the motion is periodic and angular momentum is zero for the example of three equal masses. Another question for understanding can be, as we know that the problem of two bodies…
Pipe
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