Mathematics Stack Exchange
Mathematics Stack Exchange

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.

4085 questions
3
votes
1 answer

Virasoro algebra

My question here is very computational. My problem is in mathematical physics, so I want to ask the community what kind of software they use to do the following computation if there is any? Let $$L_{n}=-\frac{n+1}{s} (u+v)n\frac{\partial}{\partial…
GGT
  • 1,045
3
votes
1 answer

How to calculate force to reach height in $t$ seconds?

I am working on a program that shoots a projectile straight up into the air. I need to be able to calculate the initial velocity required to reach a height at a given amount of seconds after firing. I know the initial velocity ignoring setting the…
Mc Midas
  • 31
3
votes
1 answer

Introduction to the replica trick

I recently came across the "replica trick\method" in the paper "Optimal storage properties of neural network models" by Gardner and Derrida. I would really like to understand it, but the problem is that the intuition used there is just from physics.…
Ofir
  • 8,015
3
votes
1 answer

Find a ratio of velocities.

The following image shows a circular disk rolling on a surface. If the velocity of a point on the edge of the circular disk is $V{p}$ and the velocity of the center of the disk is $V_{cm}$ then find $\frac{V_p}{V_{cm}}$.
user258250
  • 418
3
votes
1 answer

Changing the form of this equation

In quantum mechanics, a particle is described by its wavefunction, $y(x)$, which is related to the probability of finding the particle at position $x$ (roughly speaking). This wavefunction satisfies the time-independent Schrödinger equation,…
Jake Robertson Mckenzie
  • 31
3
votes
1 answer

How invariance is formulated mathematically?

Consider $M$ a smooth manifold of dimension $n$, then a vector at the point $a\in M$ can be defined without any reference to any coordinate system. Indeed, we define a vector $v\in T_aM $ usually as An equivalence class of curves A derivation on…
Gold
  • 26,547
3
votes
1 answer

Over what distance is transporting a box of DVDs faster than a 100Mbps connection?

This questions blends a bit of math and computer science, but I thought this would be the most appropriate SE board for it (if not please guide me to what you believe is the most appropriate board for this, as it's not programming related it doesn't…
Juicy
  • 147
2
votes
0 answers

Integral over orthogonal cylindrical harmonics

I am unsure how to solve an integral equation. As you know the orthogonality relation for cylindrical harmonics is: $$ \int_0^{2\pi}e^{in\phi'}e^{-im\phi'}d\phi'=2\pi\delta_{m,n}\ $$ The problem I have comes when you add a unit vector inside the…
Tommy
  • 21
2
votes
1 answer

Transpose of the gradient of a vector field.

Whereas I understand what the gradient of a vector field means physically, I am having difficulty understanding what its transpose actually is. I came across it in the context of defining strain in continuum mechanics (Malvern : Introduction to the…
anna
  • 21
2
votes
0 answers

negative eigenvalues for small potential

I'm reading Lieb's book "Stability of matter". On page 66 he states that for any arbitrarily small negative $V$, for $V\in L^{1+\epsilon}(\mathbb{R}^2)+L^{\infty}(\mathbb{R}^2)$ (case $d=2$) OR $V\in L^{1}(\mathbb{R}^1)+L^{\infty}(\mathbb{R}^1)$…
dan-ros
  • 179
2
votes
2 answers

Boundary conditions for second order PDE

For a second order PDE, for example heat conduction equation $\frac{\partial T}{\partial t} = \frac{\alpha}{C_p} \nabla^2 T$, is it possible to determine the steady-state (or even transient) solution with two Dirichlet conditions? I have two…
vkumar
  • 121
2
votes
2 answers

Motivation for introducing von Neumann algebra in addition to $C^*$algebra

Observables are self-adjoint elements of a $C^*$algebra. As such, this structure seems sufficient to describe physics. A theorem by Gelfand and Naimark says that a $C^*$algebra can always be faithfully represented as bounded operators on a Hilbert…
Noix07
  • 3,499
2
votes
1 answer

Solving the source free Maxwell equations for plane waves

I've been trying to solve the maxwell equations: $$\nabla\cdot\vec{D}=0,\quad \nabla\cdot\vec{B}=0$$ $$\nabla\times\vec{E}=-\frac{\partial \vec{B}}{\partial t},\quad \nabla\times\vec{H}=\frac{\partial \vec{D}}{\partial t}$$ Where $\vec{D}=\epsilon…
Freeman
  • 5,399
2
votes
2 answers

Huygens principle leads to non-uniform wave front

I'm trying to implement Huygens principle (each point of the long source is a source of spherical wave, which adds to waves from other sources) to simulate diffraction on a slit (and a grating). And when I make the slit big enough compared to…
Ruslan
  • 6,775
2
votes
1 answer

Check if a constraint is already implicit fulfilled

$\sigma_i$ is the Pauli-Z matrix acting on the $i$th qubit, hence it commutes with $\sigma_j$ if $j \neq i$. It has the eigenvalues -1 and 1. Having a list of constraints (directly fulfilled) for example $\sigma_1 \sigma_2 \sigma_3 \sigma_4 =…
nuemlouno
  • 63
1
2
3
…
12 13