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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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What set of straight ramps exist such that a ball sliding down any one of them would reach the base at the same time?

I'm looking for a set of straight ramps, which, under idealised conditions (uniform gravitational acceleration and no friction) would have a point-like body slide down them from the top to the base point in an equal amount of time. Suppose that this…
Thomas Delaney
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Euler-Lagrange - circle cone

A mass point moves on the wall of a hollow circle cone under influence of the homogeneous gravitational field of earth. Use spherical coordinates to solve this problem. a)Set up the lagrange equations of second kind. b)If the lagrange function L…
Franie Cinna
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Complex refractive index.

A linearly polarized wave with the vacuum wavelength $\lambda_0$ falls perpendicular on a material with the complex refractive index $\bar{n}=1.5+i\cdot 0.15$ with that wavelength. After what distance does the intensity fall to $1/e$th of the…
Rab
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Can someone help me to understand this formula.

Im trying to implement this in code, but I'm having some difficulties to understand it. • Using precalculation: $$\exp\left(-\frac{T}{T_f}\right) = 1 - \frac{T}{T_f} + \frac{1}{2}\left(\frac{T}{T_f}\right)^2 –…
Eduardo
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Mean-pressure of an acoustic wave

I am looking at total internal reflection for an acoustic wave, defined in terms of its pressure such that $$p = p_1 \,exp\left[-i\{\omega t-\vec{k} \cdot\vec x\}\right]$$ Using the definition of mean-square pressure, given by $$ (\Delta p)^2 =…
Victoria
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maximum position uncertainty of particle in a box

I want to verify mathematically for wave function $\psi(x)$ satisfying $\psi(x)=0$ for $\lvert x \rvert \ge \frac{L}{2} $ and $\int_{- \frac{L}{2}}^{\frac{L}{2}} \lvert \psi(x) \rvert ^2 dx = 1 $ Below holds $\int_{-\frac{L}{2}}^{\frac{L}{2}} …
Guldam
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Show that the current in a cylindrical conductor is uniformly distributed across its cross section

Using relevant equations for E and J, show that the current in a steady current I in a cylindrical conductor with uniform conductivity $\sigma$ is uniformly distributed across its cross-section. I think the relevant equations are the divergence of…
Mmm
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Center of mass of a composite body

Find the coordinates for the center of mass to the shaded out shape. How does one tackle these problems? I have tried a bunch of stuff... like considering the small halfcircle hole on the left under the x axis as negative area but I did not manage…
Nash
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Stochastic resonance

Having a look at the book Dynamical Cognitive Science, by Lawrence M. Ward, MIT PRESS, I encounter something which might be useful for my research, namely what he calls stochastic resonance, of great importance in bistable physical systems. I would…
Javier Arias
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how to calculate the phase shift in the formula that has sin in both side?

Given formula $asin ( x ) = b sin( x + \phi)$ where $a$ and $b$ are constants. I want to calculate $\phi$.
wildcolor
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Stopping point of a sliding particle.

A particle with given mass > 0 and given coefficient of friction > 0 and given initial downward speed > 0 starts at (0,1) on the graph of y = exp(-x). The coefficient of friction applies only to those points on the graph having a rational horizontal…
user27325
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Gauss Law and surface integral

Could somebody please explain to me the bottom line here. I don't understand how dS becomes r dtheta. I thought dS was supposed to be an outward pointing normal which is surely just r? I'm guessing theres something obvious im missing here.
user109331
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How can you determine Mass / kg from the attached table

I spent the last two hours trying to figure out part D and I can't get my head around it... Part D has the formula mass/kg = Mass/kg = C / ΣC I'd imagine "C" is the number of C section of the table. Does anyone know how can I calculate that…
user142516
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Non-invertible operators

Can the matrix representation of some linear operators on some vector space be singular?
SRS
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we need to find unit vector along the reflected ray.

A ray of light on a plane mirror comes along a vector $i+j-k$ The normal on incidence point is along $i+j$ we need to find unit vector along the reflected ray. I am not able to solve and draw the picture. could any one explain me what is going…
Myshkin
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