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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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Could you offer another way to prove $e^{\hat{A}}\hat{B}e^{-\hat{A}}=e^{ad\hat{A}}\hat{B}$

My professor wants me to solve this identity in two ways. Sadly, I could only do one way and haven't figure out how to solve it another way. Here is my way, Denote…
TBBT
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arrange m balls in to n baskets

How can I write a given natural number into sum of required (m) natural numbers? Example: 10=2+8+0 here m=3 Let n_i be the values i:e 2,8,0 in the above example. I want to know whether any method exists for finding ∏_i^m▒n_i ! = minimum for a given…
teja4477
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Conceptual Understanding of Kernels

In the previous thread (Difference between kernel and function?) the question of the difference between a kernel and a function came to, in my mind, an unclear conclusion. Am I right in thinking that a kernel is the property of certain functions to…
DrewW
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derivative chain rule in a triangle, confusing but interesting problem

Refer to the above figure. Assuming the length of the 3 edges of triangle are $r_0,z_0,\xi_0$. And we have $\xi=\sqrt{r^2+z^2}$ (Eqn.1)and $\xi_0=\sqrt{r_0^2+z_0^2}$. The normal vector on the hypotenuse is $\hat{n}$, and the components are…
george andrew
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Not sure what this question is asking about.

My lecturer ask me to answer this question but i can't seem to find any explanation on google after searching for quite some time.
Alex
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Using index notation

I'm trying to work out the following, but have gotten myself a bit confused I'm still getting to grips with using indices: if I have $$\bar{\nabla} \times (\bar{a}\bar{x})\bar{b}$$ I re wrote this as: $$\epsilon_{ijk}\partial_j(a_ix_j)b_k$$ But I…
Sarah Jayne
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Proving $\mathbf{E}$ and $\mathbf{B}$ satisfy Maxwell's first equation

Consider a scalar potential $\phi$, a vector potential $\mathbf{A}$, an electric field satisfying $\mathbf{E}=-\mathbf{\nabla}\phi-\dfrac{\partial}{\partial t}\mathbf{A}$, and a magnetic field satisfying…
Sarah Jayne
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General relativity from a mathematics point of view

Goodmorning, I'm a university math student. I'm quiet familiar with differential geometry and I want to study the theory of general Relativity. I try to read some books, but all of these explain the subject from a physics point of view. Could…
andreasvr
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What is the area under this graph? I am getting 2 different answers when using two different methods.

I found the area of the triangle using the formula first and got 2.25 Then found the area of the trapezium (Area of the whole graph) and subtracted the unshaded region and got 2.25 again. The third time, I split the triangle into 3 parts and found…
Maddie
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A question about John Baez's definition of "stochastic Petri nets".

John Baez, in his blog posts, introduces stochastic Petri nets as a Petri net that contains an additional function which maps each transition in the set of transitions $T$ to a real number. This function is called the "rate constant". On the other…
bzm3r
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Direct Delta Function

I was reading a Mathematics for Physics book when I saw these exercises. By using the knowledge of direct delta function, show that: $\int_{-\infty }^{+\infty }f(x)\delta '(x-y)dx=-f'(y)$ $\int_{-\infty }^{+\infty }f(x)\delta (x-y)dx=f(y)$ I have…
TBBT
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Implicit Partial derivative computation for 3rd order Runge Kutta derivation?

I need to derive the 3rd order Runge Kutta method which needs a tedious computation of partial derivatives, which i have a feeling i will make a mistake on eventually. I was wondering if there is any software or something those lines that will help…
Baklava Gain
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Stacking Cylinders Mechanics Question (from brilliant.org)

Three cylinders, all of the same mass, are stacked on a table as shown in the figure. There is enough friction between the cylinders and the table such that the cylinders remain at rest. Let Fh be the horizontal force of the table on one of the…
Lasery
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Lagrangian equations on Double Pendulum (Potential and kinetic Energy of double pendulum)

I have to prove the following equations using the Lagrangian equations, The figure shows the image, I know how to do lagrangian. I just don't know how to solve the kinetic and potential energies of this pendulum. Can someone show me what the value…
user2076774
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Why the method of separation of variables works?

The method of separation of variables is used in many occasions in the upper level physics courses such as QM and EM. But when it is used there is no clear reason why using it is permitted it except that it works, or that let us try and see. Is…
Revo
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