# Tagged Questions

"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 methods used ...

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### On Hyper-geometric Functions and its recurrence relation

I research in generating functions of Hyper-geometric functions $_2F_1(a+n,b;c+n;x)$ using Lie group theoretic method and so the recurrence relation is important in this method. I want recurrence ...
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### Schrödinger's equation denumerable eigenvalues

The Schrödinger's equation can be written in this form: $-u''(x)+V(x) u(x) = E u(x)$ $V(x)$ is a function that is defined on the real line. We know ${u}^{2}$ is integrable on the whole real line. ...
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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 ...
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### Intuition behind definition of spinor

Some time ago I searched for the definition of spinors and found the wikipedia page on the subject. Although highly detailed the page tries to talk about many different constructions and IMHO doesn't ...
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### Finding the Velocity of a Particle after an Impact

If a particle of mass $m$ has velocity $v$, its momentum is $p=mv$. In a game with balls, one ball of mass $2g$ springs with velocity $2m/s$, it hits two balls, both of which have mass $1g$, and ...
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### Identity in continuum mechanics

For a problem in the textbook I am reading, I need to prove that $\int_Vw_{i,j}v_jdV = \int_Sw_iv_jn_jdS$, where $S$ is the boundary of the volume $V$, $v_i$ is the velocity vector field of a ...
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### Falling objects - finding the speed [closed]

I am trying to work out how fast water will be falling by the time the water hits the ground. If it starts 100m high how fast would it be travelling and why? With the acceleration because of gravity ...
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### What's the probability distribution of a deterministic signal or how to marginalize dynamical systems? (functional integrals in probability theory)

In many signal processing calculations, the (prior) probability distribution of the theoretical signal (not the signal + noise) is required. In random signal theory, this distribution is typically a ...
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### Introductory book on probability for physicists

I'm a physics student looking to start learning more about probability. Is there some introductory book on measure theoretical probability theory that includes sections on quantum probability? To ...
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### Two operators $X$ and $Z$ in an infinite dimensional Hilbert space satisfying $X^2=Z^2=I$ and $\{X,Z\}= 0$

I am seeking to extend the following theorem to the case of infinite dimensional Hilbert space: Suppose we have two Hermitian operators $X$ and $Z$ in a finite dimensional Hilbert space $\mathcal H$. ...
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### Associated Laguerre Polynomials negative indices?

For the associated Laguerre polynomials/functions, it is taken (specifically when solving for the eigenstates of Hydrogen in QM) that the associated Laguerre functions with negative indices (and also ...
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### Double integral multivariable calculus

Consider the following integral $$\int_0^1 dx_1 \int_0^{1-x_1} dx_2 \, (1-x_1-x_2)^{-\epsilon-1} (-sx_2 - x_1p_1^2)^{-\epsilon-1}$$ where $s$ and $p_1^2$ are to be treated as constants throughout the ...
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### Writing 5-dimensional dynamical system as Hamiltonian system

I've got a 5-dimensional continuous dynamical system, i.e., $$\dot{x}(t)=f(x,y,z,u,w)\\ \dot{y}(t)=g(x,y,z,u,w)\\ \dot{z}(t)=h(x,y,z,u,w)\\ \dot{u}(t)=q(x,y,z,u,w)\\ \dot{w}(t)=p(x,y,z,u,w)$$ Is ...
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### Multiplying two Scalar dot products together

stackexchange community, I'm just wondering what the rules are for multiplying dot products together, such as: $$(P_{3}\cdot{P_{4}})(P_{1}\cdot{P_{2}})$$ How would this be expanded out to not ...
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### virtual work and potential energy

I was just going through the thermal and elastic buckling of bars & plates ,I found some researchers use virtual work to derive the equations, another researchers use potential energy in other ...
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### Solving Laguerre coefficients with Integral?

I'm having some difficulty understanding the solution to a particular Laguerre expansion. The problem reads "Expand the term $e^{-x}$ as a Laguerre expansion, noting the orthogonality of  < f|g&...
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### Compare analytic model with numerical, mass spring system.

So I'm trying to solve a problem here and I have been working on it all day, clearly i'm in need of some guidance. I have a rod of length $L$ and cross section area $A$, Young's modulus $E$ and ...
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### Having trouble interpreting the geometry of this setup.

A circular conductor, with cross section given by $(x-d)^2+y^2=b^2$, i.e. radius $b$ and centered on $x=d$, has a circular core, made up of the interior of the circle $x^2+y^2=a^2$, with $b-d>a$, ...
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### Finding the formula for acceleration from $v=2s^3+5s$, where $s$ is the displacement at time $t$

This is the question: I first found $\frac{dv}{ds}=6s^2+5$, then I tried to find $\frac{ds}{dt}$ by messing about a little with implicit differentiation, but I had no luck and I therefore couldn't ...
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### Acceleration of an air bubble under the sea

An air bubble arises from the bottom of the sea. Find its acceleration if the resistance force is proportional to $\rho$*A*$v$ where $\rho$ is density of water, A is cross section area and $v$ is ...
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### First Order Differential Equation for a Harmonic Oscillator

A box with mass $m$ is attached to a spring with spring coefficient $k$. This system is then placed into a glass case filled with a liquid with drag coefficient $\alpha$. Now I have the following ...
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### More equations than unknowns for maxwell equations?

I had one curiosity regarding maxwell equations in 3-D From the curl equations, you get 6 unknowns, with 6 equations. The divergence equations add 2 additional equations. When these are combined, we ...
We have the PDE $\frac{\partial u}{\partial t}+a(x,y)\frac{\partial u}{\partial x}+b(x,y)\frac{\partial u}{\partial y}=0$. What would be conditions on $a$ and $b$ for the equation to constitute a ...
I'm studying O'Neill's "Semi-Riemannian Geometry with applications to Relativity". I know that the following theorems are related to the Big Bang, but I don't understand how. Let $M$ be a semi-...