# Questions tagged [mathematical-physics]

DO NOT USE THIS TAG for elemetary 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.

2,731 questions
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### Author's derivation of time-independent form of Maxwell's equations

Laser Electronics, 3rd edition, by Joseph T. Verdeyen, gives the following: To describe an electromagnetic wave, we need two field-intensity vectors, $\mathbf{e}$ and $\mathbf{h}$, which are ...
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### Complex Analysis and Mathematical Physics

What is complex analysis used for in applied science and physics? I’m reading a book on complex analysis for a book report in AP Physics 2, for my final. I have to write a paper on it. Can anyone ...
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### Is there a construction of the Wiener measure by discretization and limits which parallels the Physics ideas?

In Physics one constructs the path integral by a limiting process together with a discretization procedure. Now, in order to better paralell with the Wiener measure, consider this in Euclidean ...
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### What kind of math should I learn before I tackle policy search PEGASUS research paper by Andrew Ng?

I provided the link below https://ai.stanford.edu/~ang/papers/uai00-pegasus.pdf the paper was referenced in the AI: Modern Approach book, and I would like to dive in depth into it. But my math is ...
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### Oscillations of an Energy Eigenstate

Energy eigenstates of a 1-dimensional particle are given by solutions to differential equations of the form $$\left(-\frac{\hbar^2}{2m} \frac{d^2}{dx^2} + V(x) \right) \psi(x) = E\psi(x)$$ where $V$ ...
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### Difference for even and odd values for $n$ in the equation system $u_{tt}=a^2u_{xx}$ and $u|_{x=0}=0$ and $u|_{x=l}=\sin\frac{n\pi a}lt$

This is a follow-up question of What would happen if the boundary value for $u_{tt}=a^2u_{xx}$ is that $u|_{x=0}=0$ and $u|_{x=l}=\sin\frac{n\pi a}lt$. In the following one-dimensional wave equation ...
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### The reason for symplectomorphism to conserve the canonical form of the Hamilton equations.

If I have $(M,\omega)$ with Hamiltonian a symplectic manifold, let $(q_1,p_1,...,q_n,p_n)$ be the Darboux coordinates. With these coordinates, the integral curves of the Hamiltonian vector field ...
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