# 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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### 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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### A computation from an article in computational neurosciences (from physical review) which doesn't fit

I am reading this article (with this erratum) in computational neuroscience, and there is a computation there that simply doesn't fit.. Maybe one of you can see something that I am missing? For the ...
I'm struggling to model this question out correctly. A glider and its pilot have total mass $230$ kg. The glider lands on a horizontal airstrip and when its speed is $16$ m/s it hooks on to the ...