Questions tagged [physics]

Questions on the mathematics required to solve problems in physics. For questions from the field of mathematical physics use (mathematical-physics) tag instead.

This tag is for questions on the mathematics required to solve problems in physics and should not be confused with those on physics concepts. Pure physics questions should go in the Physics Stack Exchange. For questions in the field of mathematical physics, please use the tag instead.

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Mathematical definition of "being a function of position"

A definition of function could be the following: A function is a tuple $(f, C, D)$, where $f\subseteq C\times D$ satisfying: $\forall x\in C : \exists y \in D : (x, y) \in f.$ $\forall (a,b), (c,d)\in f : a= c \rightarrow b = d$. Notation: If…
YoTengoUnLCD
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an integral from nonrelativistic quantum mechanics

I am trying to perform the following integral: $$\frac{1}{(2\pi)^3}\int d^3p\,e^{-i(\vec{p}^2/2m)t}\cdot e^{i\vec{p}\cdot\vec{r}}.$$ I tried like this: $$\frac{1}{(2\pi)^3}\int d^3p\,e^{-i(\vec{p}^2/2m)t}\cdot…
Wein Eld
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Power in a RCL circuit

I have an ideal RCL series circuit. How can I find the input power that the circuit needs. I know that I can write: $$V_{in}=V_R+V_C+V_L$$
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Confusing differentials problem - Electrical resistance $ R = \frac{k}{r^2} $ with $ dr = 5\% $

I am struggling with a confusing differentials' problem. It seems like there is a key piece of information missing: The problem: The electrical resistance $ R $ of a copper wire is given by $ R = \frac{k}{r^2} $ where $ k $ is a constant and $ r $…
bru1987
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Solve $y''(x)=\alpha y(x)^{-\gamma}-\beta$ when $\gamma>1$, $\alpha>0$, $\beta>0$, $y(0)>0$, $y'(0)=0$

Consider the following ODE $y''=\alpha/y^{\gamma}-\beta$ where $\gamma>1$, $\alpha>0$, $\beta>0$. Initial conditions: $y(0)>0$, $y'(0)=0$. Actually, $y(t)$ gives the position of a piston being pushed through a cylinder by the adiabatic expansion of…
Joshua Benabou
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Seesaw logic problem

The seesaw is divided equally into $6$ parts and is already tilted to the left side with the first $2$ blocks. Assuming all the green blocks weigh the same, which side would the seesaw tilt if the $3^{\text{rd}}$ block is placed on the right edge…
Truth
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Constant velocity of a sine function

I am defining the location of an object based on the sine function. The position of the object at s seconds along the x-axis is defined as x=s and its position along the y-axis is defined as y=sin(x). For example, when one second has passed x=1 and…
russjohnson09
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Line Integrals: Center of Mass

A thin wire of constant linear mass density $k$ takes the shape of an arch of the cycloid $$x = a(t − \sin t),\quad y = a(1 − \cos t), \quad 0 ≤ t ≤ 2π.$$ Determine the mass $m$ of the wire, and find the location of its center of mass. I am…
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The problem of the commutator of Hermitian operators

Well, I'm a little confused. Suppose we have three Hermitian operators $\widehat A = \widehat A^{\dagger}$ $\widehat B = \widehat B^{\dagger}$ $\widehat C = \widehat C^{\dagger}$. We know that $[\widehat A, \widehat B] = i \widehat C $ and…
user324463
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Exact period of simple pendulum.

Edit: Here is in depth derivation. Suppose the pendulum is composed of a string of length $L$ and has a point mass of mass $m$ at the end of the string. Say we incline it at an angle $\theta_0 \in (0,\pi)$ counterclockwise from horizontal…
Ahmed S. Attaalla
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Potential of a charged sphere.

Consider a charged sphere of radius $a$ and volume charge density $\rho$. Find the total work done to assemble this sphere, i.e total electric potential of this sphere. Use, $$U ={1\over 8\pi} \int_{\text{Entire field}} E^2 dv$$ I am using cgs…
user312097
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Diffusion of two interacting particles

I am reading this paper and I would like to understand how the authors obtain the equations for the prefactors $C_\gamma^\pm$ (Eq. 14 of the paper). They have to solve a diffusion problem in each region and they decompose the probability density…
A. A.
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What should $\mu$ be here in order for the logistic map to be stable?

I think this might be an error in A Survey of Computational Physics: Introductory Computational Science by Landau. On page 292, he mentions that in order for the logistic map to be stable, we must have $$\left | \frac{df}{dx} \right |_{x_*}<1$$ The…
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Need some clarification for finding work for this problem!

Q.)The resistance of a packing material to a sharp object is given by: $$F = 1.20 × 10^4 x^2$$ where x is the penetration depth. How much work has to be done to force a sharp object a distance 5.00 mm into the material? I get the fact that you have…
Nemesis
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Does the holographic principle in physics, if true, rule out the existence of infinite sets in mathematics?

The holographic principle sets an upper bound on the number of bits of information in the universe. See for example https://www.scientificamerican.com/article/information-in-the-holographic-univ/ One of the fundamental statements in set theory is…
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