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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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How do you find the number of states unlabeled particles can be in a box split in half?

I came across this problem doing research into entropy and I was wanting to simulate diffusion with a live count of the entropy of the system. In the entropy formula, you use "Ω", which is the number of possible microstates of a system (I think).…
Wensday Wensday
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Sketch the waves described by $y=(0.8\text{ meters})\sin[0.628(x-vt)]$

Ocean waves with a crest to crest distance of $10$ meters can be described by the wave function $$y=(0.8\text{ meters})\sin[0.628(x-vt)]$$ where $v=1.2 \text{ meters/s}$. a) Sketch $y$ at $t=0$. b) Sketch $y$ at 2 seconds. I believe this to have…
andy07070
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Stirling formula $\ln(n!)\approx n \ln(n)-n$ for Fermi-Dirac statistics and Bose-Einstein statistics?

I recall my teacher mentioned that you can only use the Stirling formula with Maxwell-Boltzmann statistics, not in FD or BE statistics, because of large numbers. How can you then approximate $\ln(x!)$ with FD or BE? Example approximation with…
hhh
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Which of those courses can get me to Theoretical Physics?

Im going to start a master of Maths in September and I would like some day to work in particle labs, trying to understand equations of nature etc I know which branches of maths I have liked so far (algebra, analysis, groups etc) and those that I…
Thomas
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Cubes in cubes in cubes in... ad infinitum.

Suppose I have a cube with one open side (with a volume of let's say $1\ m^3$) for the sake of simplicity; the problem is scale invariant) made from a material that makes the cube just float in water if half the cubes volume is filled with water.…
Deschele Schilder
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Centre of Mass of a Quadrant of a Square from which a Quadrant of a Circle is Cut

The wing of a hang-glider is a uniform lamina, formed by removing from a square of side $l$ a quadrant of a circle of radius $l$, with its centre at one corner of the square. Find the distance of the centre of mass (COM) of the wing from the…
J132
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Doppler effect: an understandable explanation for a mathematician

I have curiosity by Question. Can someone explain me, and to the audience too, the mathematical essence behind the so called Doppler effect? Thanks in advance. Then you have the ability to translate for example from [1], or another reference in…
user243301
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How do you swap x/y to y/x?

I saw this video on Lorentz transformation and needed to refresh my memory a bit. If $$\frac{t}{t'}= \sqrt{1-\frac{v^2}{c^2}}$$ and $$\gamma = \frac {t'}t $$ How do you make this equal ? $$\gamma = \frac 1{\sqrt{1-\frac {v^2}{c^2}}}$$ Most of you…
Tarmiac
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Circular Banked Track Friction

I've tried answering this question by resolving forces, then finding an expression for friction and inserting the given data so I can prove $F = 0$. However, I never get an answer of $0$. How do I do it?
Bob
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Triangle of forces

Forces equal to $5P$, $12P$ and $13P$ acting on a particle are in equilibrium ;find ,by geometric construction and by calculation ,the angles between their directions? I have an problem that, With three forces how can I use Lami's rule?
himu
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Equations of motion - lagrange

A mass point of mass m moves on the circle $x^2+y^2=R^2$ and $z=0$. No external forces are acting. Solve the equation of motions and determine the constraint force with the lagrange equations of first kind. I'm studying for my exams and since our…
Rafa Fafa
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Modeling $k$-logistic diffusion process

I'm trying to model a diffusion process characterized by subsequent logistic diffusion processes. To give a better idea of what I'm trying to model, you can take a look at the attached figure. In such a figure, I represented a double-logistic…
stochazesthai
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Do we deduce that the physical law isn't unit-free?

A small sphere with radius $1$ and density $p$ moves downwards with constant velocity $v$, under the influence of the gravity $g$, at a liquid of density $p_l$ and viscosity coefficient $\mu$. (The units of $\mu$ are mass per unit of length per unit…
evinda
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Normal matrix is diagonalizable

If $[A,A^*]=0$ ($A^*$ is a conjugate transpose of $A$), that is, $A$ is a normal matrix, How is $A$ diagonalizable? Or, this is just a definition of normal matrix?
cykskmy
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Quantization of Hermite differential equation

In the course of solving the time independent quantum harmonic oscillation Schrodinger equation $$ \Psi^{ \prime \prime} (y) +(2 \epsilon -2y^2) \Psi (y)$$ When we try ansartz $\Psi = u(y) e^{-\frac{y^2}{2}} $, we get Hermite Differential…
Guldam Kwak
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