# All Questions

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### Gas compressed and cooled

If a certain amount of a gas is compressed into a cylinder by the action of a piston that reduces its volume (lets say at a low speed), the kynetic energy of the gas molecules increases, what is ...
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### Understanding Tensor Product

Consider the operator $$e^{-i \hat{H} t/\hbar} = e^{-i (\hat{P} \otimes \hat{X}) t/\hbar},$$ where $\hat{X}$ and $\hat{P}$ are position and momentum operator of two different systems. We know that the ...
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### Why can't we run through walls like Harry Potter? [duplicate]

This is a very simple and stupid question but ever since I watched the first Harry Potter and saw Harry and his friends run through a wall at King's Cross Station I have wondered what keeps us from ...
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### will frictional force work against the vertical direction of velocity of an object?

We assume that an object is placed on a horizontal plane. If this object is accelerated to vertical direction, will frictional force act against the vertical direction of velocity of object? For any ...
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### Spherical magnet inside a solenoid

When passing a bar magnet through a long solenoid why is it that the induced emf when the magnet is in the middle of the solenoid is zero? And if a spherical magnet is put inside the solenoid, will ...
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### Is hydrogen atom in a box solvable analytically?

Schrödinger's equation for hydrogen atom in free space can be easily solved by switching to center of mass frame, introducing reduced mass and separating variables in the resulting 3D problem. But ...
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### Would cereal still group together if it were suspended in the liquid (milk) - rather than floating on top?

According to my interpretation of several online sources (correct me if I am wrong), cereal tends to group together in our bowls of milk because it creates a deformation on the surface of the liquid ...
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### Concrete example of Earnshaw's Theorem

I'm struggling to understand Earnshaw's Theorem. I've tried reading the original paper, and the wikipedia article. I know enough math to be able to understand the mathematics of the theorem, but I ...
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### Heat loss from hot cast iron oven

I am considering an unconventional pizza oven made from cast iron. What is a good formula for estimating non-radiative heat loss from a 450C/850F surface in a 20C outdoor environment? I am looking ...
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### Gravitational singularity

Is it possible that the gravitational singularity actually turns out to be a genuine singularity once we have a true theory of quantum gravity in place. There is a lot of talk about singularity but ...
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### How to express the differentiation of an antisymmetric matrix (the HFB pairing field)?

I'm trying to wrap my head around the differentiation of antisymmetric matrices in the context of Hartree-Fock-Bogoliubov (HFB) mean-field theory (see also e.g. Ring & Schuck, Blaizot & Ripka, ...
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### liquid trapped in wet sponge

If you soak a sponge in water, or some other liquid, and then let it hang then some liquid will flow down due to gravity but not all, some amount will remain trapped in the sponge by the capillary ...
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### When will be a suspended (not at the center of the mass) symmetric rotating gyroscope in stable or instable position?

The original question is what is in the title. I'm not sure about the answer so here is my solution, please correct me If I am wrong: It is known for a gyroscope what is in a homogenous gravity field ...
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### Lagrangian with a boundary contribution, external work and interaction

I am considering a linear second order partial differential equation of the form \begin{align} F(q,p)&=-a\,q-\nabla\cdot p=0\\ p(q,\nabla q)&=b\cdot\nabla q \end{align} with $a$ scalar and $b$ ...
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### Bypassing complementarity with cumulative weak measurements?

Consider the standard double slit experiment with one photon at a time. Now, replace the photographic plate (or fine resolution single photon detector screen) with a converging lens, and move the ...
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### What is the different between topological order and Landau's order in a system

I have thought about topological order for a long time, but I am still confused it. Roughly speaking in my understanding, the topological state is the eigen-state of some special symmetry such time ...
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### Why are LCDs black? [duplicate]

I had a question on LCDs after noticing something interesting about its color. LCDs are black when they aren't used. But when we observe LCDs closely, we see they are made up of red, green, and blue ...
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### In Rational Gaussian Model, why must $R^2$ be rational?

I am reading Fusion Rules and Modular Transformations in 2D Conformal Field Theory and Verlinde talks about the rational gaussian model. The simplest class of RCFT's are the rational gaussian ...
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### Klein-Gordon field commutator integral identity [closed]

Consider a Klein-Gordon field $\phi$ on points $x,y$ of $\mathbb R^4$ Minkowski-spacetime. Here I'm writing $x=(x^0, \stackrel \rightarrow x)$ so that $\stackrel \rightarrow x$ gives the spatial ...
A ball of mass $m$ travelling with a velocity $v_0$ collides elastically, and perpendicularly with a rod at a distance $d$ from the center of the rod. The rod has a mass $M$ and lies on a frictionless ...