Position Definition and 1000 Threads

Suppose I have an initially localized free particle at x0 then I measure its momentum it will become a plane wave so there is a probability that if I measure its position again to find it far away from its initial position if the time between the two measurements were T isn't finding the...

Let the representation of a Hermitian Operator in some basis ##x## be $$\hat A\equiv A(x)$$ and let $$\psi(x)=\langle x\vert\psi\rangle$$ Then we define $$A(x)\,\psi(x)=\langle x\vert\hat A\vert\psi\rangle$$ This is the Wikipedia article that mentions this. From here how do we derive the...

I've been doing astronomy for Science Olympiad for a few years now and know all the basics about DSOs, HR diagrams, etc. However, I've only recently acquired a telescope since I thought it would be nice to locate some DSOs independently. I understand how RA and D are calculated, but I am not...

For this problem, My solution is However, the my answer for ##\Delta x## is not correct. The correct answer is ##\Delta x = 0.18a##. Does someone please know what I have done wrong? Kind wishes

In special relativity, is the derivative with respect to coordinate time of relative position equal to relative velocity? Does it matter if constant velocity is used?

I have an encoder that measures the rotational angle of a shaft. The problem is that the other end of the shaft can move in X and Y (forward/backward and left/right) as well as rotate. Assuming I can get couplings to link the shaft to the encoder and the moving item, will the encoder always...

I first calculated the time using y = (viy)(t) + 0.5gt^2 where y is the vertical displacement which is 0 for the ball landing back on the ground, viy is the initial vertical velocity ie 16.55m/s and g = -9.8m/s}^2. I get 2 values for t, t=0 and t= 3.377s. Then using the equation x = (vix)(t) =...

I have a database that looks like this: I want to get the "leaderboard position" of a particular member. The idea is to order the data by the score column, and then retrieve the row position of that particular member id. This is my query in MySQL: SET @rowNum := 0; SELECT rowNum FROM(...

If we consider ##v=-3t^2## then: $$x=-t^3$$$$a=-6t$$ Using ##t=-x^{1/3}## we have : ##a=-6(-x^{1/3})=6x^{1/3}##. My answer suggust that ##F=Ax^{1/3}## but in options we have ##F=-Ax^{1/3}##. Can someone guide me where my mistake is?

My attemp : ##\vec r_1## : Position of the river in reference frame. ##\vec r_2## : Position of the walker in reference frame. ##\vec r_x## : Position of the walker measured by the river. We have: $$\vec r_1 + \vec r_x = \vec r_2$$ $$\vec v = \dfrac {d \vec r}{dt} $$ $$\vec v_1 + \vec v_x =...

How do you derive the position vector in a general local basis? For example, in spherical coordinates, it's ##\vec r =r \hat {\mathbf e_r}##, not an expression that involves that involves the vectors ## {\hat {\mathbf e_{\theta}}}## and ## \hat {{\mathbf e_{\phi}}}##. But how would you show this?

position and velocity expressions for the initial conditions 1) x(0)=Acosφ = xi 2) v(0)=-ωAsinφ= vi Dividing 2nd equation by equation results in: -ωAsinφ/Acosφ = xi/vi tanφ = xi/(-ωvi) tanφ = 0.4 And here they (the textbook) got φ = 0.127π, This is where I...

The peak of the radial probability density for the 1s state is at the Bohr radius ##a_0##. But if we consider equal volumes as cartesian boxes, can one fairly say the electron has a higher probability of occupying a box near the nucleus than elsewhere because the peak of ##\psi^* \psi## is at zero?

I know how position and momentum commute, but now I have the spin angular momentum operator involved as well as a dot product. Specifically, what would the commutation [x,S·p] be?

Why there will be no change in potential energy due to this sharp blow ? Potential energy is a function of position , so won't this position get changed due to this sharp blow?Please help!

In the lab, how accurately can we measure momentum? What is the max value of the uncertainty in position as the uncertainty in momentum approaches zero? Or vice versa. What experiments do these types of measurements?

This is how I am approaching the problem let the lightpen be at a position (x,y) and the position to be plotted(x1,y1) The the time lag = (1/60)*(90/100)*(1/1024)*(90/100)*(1/1024)*(1024-x)/1024 ->for lightpen to complete the horizontal trace + (1/60)*(90/100)*(1/1024)*(1/10) ->...

Is my work correct? I got confused whether the current Splits or not, but i decided against it.

Even though I have all the formulas needed to do this problem, I cant figure out how to get rA, rB and rA' aswell as rB'

At first I thought that this force vector ## \vec F = 3 \hat x + 2 \hat y ## is a function of ## x ## and ## y ##, which is to say that its magnitude and direction vary with the x and y positions, but this is not so, right? It's just a force with a constant magnitude and direction. And I can...

Hi, I was wondering if you could help me with a job at the university that consists of the kinematic modeling of mechanism number 3 in the image attached to this message. I have to set up the constraint equations and then solve the position, velocity and acceleration problem. For now I would...

Question: Suppose that two bodies of masses m1 and m2 are a fixed distance d apart, and that both of them act on a third body of mass m. Find the position of the third body such that the two forces are in equilibrium. I have solved this question and obtained the answer listed in the back of the...

What is ##<x|P|x'>##? (for particle in 1d, and ##\hbar = 1##)?\begin{align*} <x|P|x'> &= \int dp' <x|P|p'><p'|x'> \\ &= \int dp' \ p' <x|p'> <p'|x'> \\ &= \int dp' \ p' \frac{1}{\sqrt{2\pi}} e^{ip'x} \frac{1}{\sqrt{2\pi}} e^{-ip'x'} \\ &= \frac{1}{2\pi} \int dp' \ p' e^{ip'(x-x')} \end{align*}

Hello! I am doing some calculations and I would like to use the best value for a micro channel plate (position sensitive) position resolution to date. I don't care too much about the details, but I don't want to use too small of a value and of course I'd like to give a reference for this value...

A simultaneous measurement of both a particle's position and momentum may be successfully accomplished if more than one photon were utilized for the measurement. A non-demolishing measurement is possible if the emitters were aligned such that each would offset the other’s recoil of the target...

Hi everyone, I have started delving into the "nightmare" of source definition and in my opinion, the MCNP manual here sounds even more cryptic and obscure than in other sections. By the way, I have a question related what is reported in paragraph 5.8.1 of the MCNP® Code Version 6.3.0 Theory &...

To get expected value I use $$E = \int \Psi^* Q \Psi dx$$ where Q = x $$4a^3 \int xe^{ax} \cdot x \cdot xe^{-ax} dx = 4a^3 \int_0^{\inf} x^3 dx$$ which is undefined. But the answer is suppose to be 1/a.

Hello, so we have two potitions right, if we take ##\theta = 90## as the first position (i.e. both rods are flat) and then the second position at ##\theta = 0##. I totally understand the exercise, not difficult. The only issue I am having is the torsional spring... it says that it is uncoiled...

So the pattern goes: x(t) v(t) a(t) jerk(t) You can keep taking slopes of lines, and slopes of slopes - my questions is, what happens in the other direction- areas under curves and more areas under curves. What is the area under the x(t) curve? x*t, what is position multiplied by time?

Hello everyone. This is my first post here. I hope that you had a good Christmas eve and that you are in good health. Recently I graduated with a B.S. in Mechatronics Engineering, and I got a job in a local manufacturing company in my hometown. Before proceeding with the post, I want to say that...

The answer is E. I was initially very confused as to why the answer was not A but realized that the graph was velocity vs position (rather than velocity vs time) which means I can't simply take the derivative of the given graph. One thing I tried was writing out the equation first(c being a...

Hi, I asked this question elsewhere, but I didn't understand the answer. It seems to be easy to understand, but for some reason I'm really confuse. I'm not sure how to find the average position of an electron and the average separation of an electron and his proton in a hydrogen atom. To be...

For this problem, How did they get that formula shown? My working is, All the solutions wrote was, Many thanks!

I would like to read a specific line of a file. Everything I have seen does it by reading the file from the top, ignoring what is read until the line of interest is reached. Is it possible to move the pointer of the reader to the line directly, say by counting the number of line end sequences...

I am trying to determine how the addition of a counterweight affects the ##C_m-\alpha## (in longitudinal direction) graph for a model plane project, where the counterweight can be considered as the battery. Suppose we try to place the battery at the back of the current CoM. The new CoM will...

Good evening, I have a question on the problem I've provided in the homework statement. Essentially, the problem is asking us to compare the maximum height and time to max-height between a simple projectile motion case vs. a case using fluid resistance proportional to v. I've solved everything...

I'm currently reading the expanse and thinking a lot about how the spaceships are built. As far as I understand, the cockpit and control room sit on top of the ship (with the ships beeing built like skyscrapers). Now since there are no windows, I feel like the cockpit doesn't need to be in the...

Good morning all! I have a quick question regarding high voltage transformers, can someone explain why we need to put the low voltage winding the closest to the core and the high voltage winding on the "outside"? Have a nice day!

for 3di i did the normal AB=BC so b-a would give either satisfy or not this phenomenon, my answer was (3a-1, -4) & (2a^2 + a - 1, 4a - 2), now how would i know from here if they're collinear or not?

Hello guys, I don't know if this is the right place to ask, so please be kind :/ I have a question regarding the location of an electron that belongs to an atom. A teacher told me that the probability of an electron to be found within its orbital is around 99%. When I asked about the remaining...

Good Morning! I understand that a vector is a physical object I understand that it is the underlying basis that determines how the components transform. However, I encounter this: https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors The fifth paragraph has this statement A...

Hello everyone, I would need help to model a motorized system controlled in a closed loop. It is a personal project. At first, I am looking to obtain the transfer function and simulate the system on computer. In a second step (not the aim of this thread), I would like to use this simulation to...

Hartle, Gravity "An observer in an inertial frame can discover a parameter ##t##with respect to which the positions of all free particles are changing at constant rates. This is time" Then goes on to say "Indeed, inertial frames could be defined as Cartesian reference frames for which Newton’s...

Hello, On the image below is a test pendelum for rock wool production. The pendelum is driven by two induction motors. When the right motor makes one revolution, the left motor makes two revolutions. The motors are positionally locked (example: when the right motor is at 35.3° the left motor is...

Suppose we have a large sphere with thin non rotaring surface of floating iron particles (to prevent that they start a chain reaction making a star instead of a black hole) with a total mass sufficient to form a black hole. with an observer in the center of the sphere. This means the sphere...

How is it possible for a particle to be in two different states/places at the same instant?

what would be the y'-x' ##\vec r## vector be? I think it is ##\vec r = (8t - 1) \hat i + (6t - 2) \hat j## (not sure whether it is correct or not.) I thought about it as at t = 0 the position needs to be -1i -2j so that is why I took the signs in the y'-x' frame position vector as a - instead...

I have attempted the problem a few times, and have posted my work below. I thought to check my work using ## v_x t = v_1 \times \cos\theta \times t = \Delta x## to see if I get back expected results, and I did for the horizontal motion (the substitutions are from the numbered steps below): ##...

Using the data given and recalling that in this configuration ##R<0## I get: ##\frac{1.33}{0.5}+\frac{1.5}{q}=\frac{1.5-1.33}{-0.2}\Rightarrow q\approx -0.427 m=-42.7 cm## so the image is virtual and is ##42.7\ cm## to the left of vertex ##V##. The magnification is ##M=\frac{n_1 q}{n_2...

We usually have an initial time and then find an equation for the variable final time. Can we derive a formula to calculate position with final time and variable initial time. ##v = v_i + a(t_f - t_i)## ##dx = v_idt + at_fdt - atdt## integrating ##x_f - x_i = v_i(t_f - t_i) + at_f(t_f - t) -...