Mean Definition and 1000 Threads

As we always say eat food and rest because tomorrow you have to go to work. When we throw a ball up, it gains a max PE at some height. More the height more energy it has which makes it do more work. Is this right to say?

I've a Gaussian momentum space wavefunction as ##\phi(p)=\left(\frac{1}{2 \pi \beta^{2}}\right)^{1 / 4} e^{-\left(p-p_{0}\right)^{2} / 4 \beta^{2}}## So that ##|\phi(p)|^{2}=\frac{e^{-\left(p-p_{0}\right)^{2} / 2 \beta^{2}}}{\beta \sqrt{2 \pi}}## Also then ##\psi(x, t)=\frac{1}{\sqrt{2 \pi...

Hello! If I have N points (x,y) which I know they are described by a Gaussian i.e. y(x) is a Gaussian of unknown mean and standard deviation, and each y has an associated error of ##\sqrt{y}##, is there a general formula for the uncertainty on the mean of this function? Thank you!

[Moderator's note: thread spun off from previous thread due to topic/level change.] This [Ed.: the claim that photons have a "path"] is a misconception of quantum theory already for massive particles. It's even more severely misleading for massless quanta of spin ##\geq 1##, which do not even...

I don't need an answer (although I don't have sadly, it's from a test). I need just a tip on how to start it... i cannot use Taylor in here (##\ln(x)## is not Taylor function), therefore, its only MVT, but I don't know which point I should try... since I must get the annoying ##\ln(x)##...

I know that we can change the spin orientation of a spin 1/2 particle up or down and test it in the Stern Gerlach apparatus. And the spin 1/2 particles need two full rotations to return to the previous state. Questions: 1). what does state mean? 2). Is, Changing spin orientation to up or...

Suppose f1,f2... is a sequence of functions from a set X to R. This is the set T={x in X: f1(x),... has a limit in R}. I am confused about what is the meaning of the condition in the set. Is the limit a function or a number value? Why?

https://pubmed.ncbi.nlm.nih.gov/24995959/ What does it mean by PC in this article?

how does the first step use mean value theorem? I don't get it , can anyone explain , thanks.

Find the textbook problem here; Find the textbook solution here: Now, to my question, did the textbook guys make an error on the value of ##σ?##, see my working; Mean (##13## boys)=##\dfrac{153.4+(148.8×12)}{13}=149.15## We know that, ##29.16##=##\dfrac{\sum x^2}{12}##-##(148.8)^2## ##\sum...

Hey! :giggle: We consider a double roll of the dice. The random variable X describes the number of pips in the first roll of the dice and Y the maximum of the two numbers. The joint distribution and the marginal distributions are given by the following table Using : For all $a,b\in...

I understand everything except operational security. What is that trying to say?

(I am not sure which forum this post belongs to. Hope someone kindly helps me move it to a proper forum.) In papers, for example, here, here, and here, the authors start from the Lagrangian for matters and gravitational fields, then Dirac's constrained canonical quantization is used. They...

I have a graph of mean signal (per pixel) vs exposure time (sec) for 8 different dark frames. I am being asked to find the bias in ADUs/pixel and the dark current in ADUs/sec/pixel and I am very confused on how I could get it. I know that the average of all of the mean signals is a rough guide...

It's my (limited) understanding that your immune systems responds to most (all?) microbial threats initially with aches and fever, i.e., that these initial symptoms are not caused by the microbe but by your immune system's activation. So what does it mean if one is infected and infectious but...

I'm reading a book called "Reality is not what it seems: the journey to quantum gravity" by Carlo Rovelli and I'm struggling to understand this diagram that is part of the chapter about special relativity. https://i.stack.imgur.com/JgBDJ.jpg Before this image Rovelli writes: "It's not...

lambda (rms)= v(rms) * t(rms) -- 1 Now I assume here that t(rms)=1/(√2*n*π*d^2*v(rms)) But this cancels the v(rms) term when used in eq (1) so the mean free path and the RMS free path would actually be the same (even later on when used in the aforementioned Survival Equation) I would like to...

Hi, there. I encounter the word "foliate" in GR textbooks but I have not seen it in other physics textbooks before. For example, it reads, we argue that a spherically symmetric spacetime can be foliated by two-spheres, from page 197 in spacetime and geometry by Carroll. By this sentence, I...

why is answer for (6a)6J?

they said that Y is acting as the ground, what does it mean?

1. μ* is easily calculated to be 100.88, textbook confirms its 100.9. Its just the mean of all those values. 2. To estimate mean error I first calculate s^2, which is: $$s^2 = 1/7 * ((115 - 100.9)^2 + (82 - 100.9)^2 ... + (92-100.9)^2) = 1200.88$$ $$s = \sqrt s = 34.65$$ Then I use this...

But then I learned a photon can be split into two or even three photons (red-shifted, energy is conserved), and also photon can lose energy and still be a photon (Raman effect, inelastic scattering). Now, I am not sure what it means when it is said photons are quanta of light (smallest unit of...

I saw it somewhere but I did't know exactly what it meant. Could someone explain it to me like I am 5? Does it mean we integrate with respect to x n times? $$\int_{\mathbb{R}^n}f\, \mathrm{d}^n x$$

Is Mean Temp in 2 phase Heat Exchangers Higher Than Logarithmic Mean? I am looking at this paper: https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1314&context=iracc Having a bit of trouble understanding all of it, but my basic question is just: If I have a heat pump where the hot...

Hello, there. I am studying a model for decoherence of two entangled photons. The space for the first photon is 2 dimensional, while that for the other one is 6 dimensional. In total, the system will be in a 12 dimensional space. Initially, they are set to one of the Bell states, such as...

We have the area of incandescence. Using that we can find the radius and subsequently the diameter. A=π* r^2 -----> r= 0.0025m so d=0.005m Using the formula (given by Clausius as we are not specified in question whether it's a Maxwellian distribution or not) Mean Free Path λ=...

Just saw a documentary about resolving Hawking's "information paradox". In my own lay terms the physicists appear to theorize resolving the paradox with with their proposed C = 12 J . C is the central charge (which I don't fully understand) and J is the total angular momentum of the black...

I understand that electronegativity and electropositivity are opposite terms, but does being high in one mean you are low in the other? I saw that HCl will react with NaCl to create Cl2 and NaH. I believe that Cl has the greatest electronegativiy (willingness to attract an electron). So...

Hello, I would like to know the right expression for the expression of variance of Shot noise in spectroscopic probe. Sometimes, I saw ##\sigma_{SN,sp}^{2} = 1/n_{sp}## with ##n_{sp}## the average density of galaxies, whereas my tutor tells me that ##\sigma_{SN,sp}^{2} = 1/n_{sp}^{2}## , so I...

When I was following the calculations of finding the potential energy of a spring standing on a table under gravity, I encountered the integral shown below, where ##d\xi## is the compression of a tiny segment of the spring and ##k'## is the effective spring constant of that segment. The integral...

'Every non-equilibrium state of a system or local subsystem for which entropy is well defined must be equipped with a metric in state space with respect to which the irreversible component of its time evolution is in the direction of steepest entropy ascent compatible with the conservation...

That is how I understand curl: If I have a vane at some point ##(x,y)## of a vector field, then that vane will experience some angular velocities in points 1 ##(x+dx,y)##, 2 ##(x,y+dy)##, 3 ##(x-dx,y)##, 4 ##(x,y-dy)##. Adding those angular velocities gives me the resulting angular speed of...

While I will not be showing the graph here, I am trying to dissect what the question even means. While I do understand that relative uncertainty can be found via the equation ##\frac{\sigma_A}{A}##, I do not understand how I can find the "relative uncertainty of SEM". Does anybody here have any...

Yes, heat can flow into a body without increasing the mean kinetic energy of its molecules. Transferring heat energy to an object will raise its internal energy, this will not necessarily cause an increase in temperture. Specific latent heat is the energy required to change the state of one...

A pair of spins described by the product operators ##I_{1x}I_{2z}## are said to be anti-phase, while ##I_{1y}I_{2y}## are in phase. What does it mean for a pair of spins to be anti-phase with each other, when their spatial vectors representing direction are orthogonal in space? Under coupling...

I am learning about the use of Monte Carlo to calculate/estimate uncertainties. If I take the example of a single measurement (i.e. I measure several quantities required to get an estimate of some physical property, but I do this only once), I can use Monte Carlo and some common sense for the...

So I have an excellent memory. It’s not eidetic but I remember minuscule details that other people shouldn’t. I always did pretty decent in school but I was weak in math. I am a grad student currently going for a degree in Library Sciences. My IQ was tested as a toddler and it was a little above...

I am sorry if this is a silly question, we know that- Electric Charge is a characteristic property of a Subatomic particle. And, a body is electrically charged by the transfer of electrons. Then, what does it mean by this the charge on a body is denoted by q.What are we talking here. Are we...

When physicists talk about a theory having local degrees of freedom, what is exactly meant by that statement? What are examples of theories with local degrees of freedom and what are examples of theories with no local degrees of freedom?

I know about these metrics Euclidean metric Einstein manifold Riemannian, pseudo-Riemannian manifolds or Riemannian space Lorentzian manifold Minkowski space Kähler manifold Schwarzschild metric Kerr, Kerr–Newman metrics Reissner–Nordström metric inverse or conjugate or dual metric Induced...

Electric Charge is the characteristic property of subatomic particles that causes it to experience a force when placed in an electromagnetic field. So, if electric charge is a characteristic property of subatomic particle then- what do we mean when we say charge is transferred from one body...

I found the mean to be $$\langle n\rangle=\vert\alpha\vert^2 \tanh(\alpha^2)$ and $\langle n^2\rangle=\vert\alpha\vert^2 \left( \alpha^2\sech(\alpha^2)^2 + \tanh(\alpha^2) \right)$$. Do you know if there is any reference where I can check if this is correct?

Consider the Schrödinger equation for a free particle: \begin{equation} -\frac{\hbar^2}{2m} \partial_i^2\psi = i\hbar\partial_t \psi. \end{equation} Let us be interested in the motion of a free particle in quantum mechanics. We say ok, we have a solution to the Schrödinger equation for a...

Does mean velocity of particle equal group velocity of wave packet in QM?If they do not equal which of them is classical velocity?

Here's a list of six numbers written in order of size 4, 7, x, 10, y, y The numbers have a median of 9 a mean of 11 Find x and y? So I've gone to do: (4+7+x+10+2y)/2 = 11 I get x+2y = 45 What do I need to do from here?

I'm a current high school student and I’m aspiring to become a biochemist. I’m at the moment writing an article about adaptive mutations but there is a lot of tricky quantum mechanics in it which I simply don't get. I have asked everyone and got no answer until someone recommended to ask it in a...

In the wikipedia article of the observable universe I have read the following: "Both popular and professional research articles in cosmology often use the term "universe" to mean "observable universe". This can be justified on the grounds that we can never know anything by direct...

If Hamiltonian commutes with a parity operator ##Px=-x## are then all eigenstates even or odd? Is it true always or only in one-dimensional case?

When we say that x∈R does here x represents all real numbers at the same time or x represents only a single real number at one time. How can a single variable(x) represent all the real numbers at the same time ? when we write x∈R it means that x is an element of the set of real numbers, this...