Position Definition and 1000 Threads

The attempt ##\int_{-\infty}^{\infty} |ψ^*(x)\, \hat x\,\psi(x)|\, dxˆ## Using ˆxψ(x) ≡ xψ(x) =##\int_{-\infty}^{\infty} |ψ^*(x)\,x\,\psi(x)|\, dxˆ## =##\int_{-\infty}^{\infty} |ψ^*(x)\,\psi(x)\,x|\, dxˆ## =##\int_{-\infty}^{\infty} |x\,ψ^2(x)|\, dxˆ## I'm pretty sure this is not the...

Hi, In another forum someone asked how to find the kth digit of a large prime given in the form ##2^t-1 ## , where t is a 6-digit (decimal) number. I was thinking maybe using some SQL string function , though I am not sure if input strings must be entered explicitly. Can anyone think of some...

Hi, can anyone see if I have made an error in answering this simple question, my answer is not the one given in the textbook. Here's my diagram of the system in equilibrium. So the mass has dropped a distance x below the midpoint of PQ: So the forces balance as: T1 = g + T2 So, using...

Motivation: In my thermodynamics + statistical physics class, we derived the equipartition theorem for ideal gasses using Boltzmann factors, dividing the phase space of a gas particle in position+momentum space into units of size x*p=h based on the quantum nature of the space of states that are...

I am trying to use the Method of images for this configuration, But somehow I don't know where should I put the imaginary charge. I know the on the surface of the conductor the potential must be zero and the imaginary charge should be other side of the conductor but that's all I cay..

Hello, regards to all. I am designing a CNC machine where the table will work as a Z axis. I have found a complication when trying to save space under the table, to avoid set the ballscrew upright I have decided to make a scissor mechanism but I have noticed that when the ballscrew travel 10mm...

I) For ##A##, the positition is ##\vec r=(0;V_0 . t;0)##. For ##B##, we have ##\vec r_A=\vec r_B + \vec r_{A/B}##, but ##\vec r_{A/B}## is equal to zero because they have the same origin, so the position measured from ##A## is equal to the position measured from ##B## II) For ##A##, velocity...

At the beginning of every course in QFT we are told that, unlike in ordinary QM in which the position variable is a physical observable , the position variable in QFT is just a label. Yet there are areas within QFT where the position variable is treated like a real physical degree of freedom...

In QM a free micro particle with definite momentum has not definite positions.But why does in classical physics a free particle with definite momentum still have definite positions but not blurred as in QM?(Because we can deduce Classical Physics from QM)

This is a homework question from my friend, I found the time but a tough differential equation occurred when I was trying to find accelaration, is there a simple solution for this?

Well, ##r(t)## in ##A## is just a vector ##(0;y)## because is tangent to the trajectory. Then, from the perspective of ##B## the particle moves in an uniform circular motion. Is this right? The velocity from ##B## must be ##\omega##, right? And what about acceleration?

Would it be correct if I multiplied the time by the velocity of the object since the units would cancel into meters? So for example, I multiply 2 seconds by 1m/s which gives me 2m - would that be the object's position?

Recently I have come into Special Relativity and specifically Lorentz transformation. Let's assume two frames A and B moving relative with speed ##v##. The position of a particle moving with respect to B is given by ##x′=f(t′)=3t′##. What is the function of position ##x=f(t)## of the particle...

Suppose we have a reversible reaction $$aA + bB <=> cC + dD$$ which is exothermic in the forward direction. If the temperature of the system decreases, the rate of the forward reaction will increase so that the quotient Q increases to the new (higher) value of Kc. This I think I am ok with (I am...

For part a I used conservation of energy. -m*g*cos(θ)*L+1/2*m*0^2=-m*g*L +1/2*m*v^2 => v = sqrt(2*g*L(1-cos(θ )). b) For b I was think that T = mg in the equilibrium point but that doesn't invole θ in the answer. So that's why I tought that T*cos(θ ) = mg. So that the tension is mg/cos(θ). But...

Why can't the general state, in the presence of coupling, take the form $$\psi_-(r)\chi_++\psi_+(r)\chi_-$$ where ##\psi_+(r)## and ##\psi_-(r)## are respectively the symmetric and anti-symmetric part of the wave function, and ##\chi_+## and ##\chi_-## are respectively the spinors representing...

Let us suppose we have a line ##l_1 = ax + by + c = 0## and we have a point P, ##P(x_p, y_p)## that is outside of this line. If we draw a perpendicular line from point ##P## to a point on the ##l_1##. What would be the coordinates of this point ? I know there are many ways to do it. But I am...

I don't know if this question suits this forum, I post this here actually because I saw (if not my memory is failing) that here it is also possible to solve math problems. So, back on track: I like to discover things from myself, so I searched for the Euler's formula, willing to find the...

Summary: Rotate a shape back to it's original position with the least amount of rotations. Lets say you have a cube. It's starting rotation is (0,0,0). It can be rotated on each axis ( x,y,z ) no more than once each by 90 or -90 degrees (rotation can also be skipped for any axis). The shape...

2.62 An object's velocity is measured to be $v(t)=\alpha-\beta t^2$ where $\alpha=4.00\, m/s$ and $\beta=2.00 \, m/s^3$ At $t=0$ the object is an $x=0$. (a) Calculate the objects position and acceleration as functions of time (b) What is the object's maximum positive displacement from the...

A square sheet of metal has a square of one quarter of the original area cut from one corner as shown in the figure. Which of the following statements is true about the position of the centre of gravity of the remaining portion of the sheet? a) center of gravity lies at a distance of 5/12 of...

Hi! I am trying to change the hydrogen ground state wave funcion from position to momentum space, so i solved the integral Ψ(p)=(2πħ)^(-3/2) [SIZE=16px][FONT=Noto Sans](πa^3)^(-1/2)∫∫∫e^(prcosθ/ħ) e^(-r/a) senθ r^2 dΦdθdr and got 4πħ(2πħ)^(-3/2) p^(-1) (πa^3)^(-1/2) I am [(ip/ħ-1/a)^(-2)]...

I am talking about low wing single engine WWII fighter types. In particular, I am interested in accelerated propeller airflow through the transition/curvature of the prop slipstream spiral distribution around the wing, from being partly below, towards mainly above the wing. This as the wing's...

I know that the height before the first bounce will be ##y = g * t * t + v_0 * t + y_0##. After the first bounce, I can find y by pretending the ball was thrown from the ground with velocity ##e * -v_f## with ##v_f## being the velocity of the ball when hitting the ground, but I have to reset the...

here I am trying to find ##\frac{d}{dt}dx## where ##x(t)## is the position vector Now ##\frac{d}{dt}(v_x(x,y,z,t)dt)=\frac{dv_x}{dt}dt=\frac{\partial v_x}{\partial t}dt+\frac{\partial v_x}{\partial x}dx+\frac{\partial v_x}{\partial y}dy+\frac{\partial v_x}{\partial z}dz## Now dividing by ##dx##...

In https://en.wikipedia.org/wiki/Lamb_shift about the lamb shift, it's mentioned that the change in the electron's frequency due to QED effects (vacuum polarization and self-energy correction) is about 1 GHz, which would translate to an energy change of hf = 6.63E-25 J. This is 3E-7 times of the...

I have read on Wikipedia (https://en.wikipedia.org/wiki/Compton_wavelength) that we cannot measure the position of a particle more precise than half of its Compton wavelength, since the photon we would need will be so energetic to produce electron-positron pairs. How does the creation of...

Why was it important that both arms were parallel and perpendicular to the rotation of the earth?

I tried by taking the derivative of the potential to find the critic points and the I took the second derivative to find which of those points are minimum points. I found that the point is ##x=- a##. I don't understand how to calculate the period, since I haven't seen anything about the harmonic...

Hello all, I have a question with the helix path of proton in a magnetic field that I am a bit stuck on. Question: Equations: F = qv X B F = mv^2/r d=vt My Attempt: Think the graph drawn is good enough for questions (a). However, I am stuck on (b) and (c). Firstly I am not entirely sure...

Homework Statement From Griffiths GM 3rd p.266 Consider a free particle of mass ##m##. Show that the position and momentum operators in the Heisenberg picture are given by$$ {\hat x}_H \left( t \right) ={\hat x}_H \left( 0 \right) + \frac { {\hat p}_H \left( 0 \right) t} m $$ $$ {\hat p}_H...

Homework Statement A 39,000 lb truck A and a 3968 lb sports car B collide at an intersection. At the moment of the collision, the truck and the sports car are traveling with speeds vA = 70 mph and vB = 30 mph. Assume that the entire intersection forms a horizontal surface. Letting the line of...

Homework Statement Hello today I am solving a problem where an electron is trapped in a potential well. I have a solved Schrodinger's Equation. I am having problems in figuring out what the wave function should be. When I solved the equation I got a complex exponential. I know I cannot use the...

Homework Statement Three spheres are placed around a coordinate grid: one of mass m at the bottom-left, one of mass 3m a distance of 3L above the first, and one of mass 2m a distance of 4L to the right of the first. 4 points between these three spheres are labeled: A near (1.3L, 1.5L), B...

Hi, I am studying the behaviour of a pulley that is attached to a sling. The situation looks like this: There is a drum that can give or take cable. Then there is a floating pulley with a cable through it. The pulley can move on the circle with a radius the same as the length of the sling...

H(t) = t^3-6t^2+5t+30 this is a yo yo 30 inches above ground at t =0, at 4 secs it is 18 inches above ground. Please tell me how these figures are derived; t^3,6t^2, 5t; I realize the 30 is initial position. I am 81 but very curious. Thank you.

I was reading a book which had some comments on EPR paper (Einstein, Podolsky, Rosen - 1935) like following: In Newton's physics, when two identical billiard balls hit each other head-on, bouncing off in opposite direction, knowing one ball's position and speed will also indicate other ball's...

Homework Statement The position vector of a particle changes: Only by its module. Only by its direction. What can be said about the trayectory of the movement of the particle? Obtain the answer analitically. Homework Equations None. The Attempt at a Solution I think that the trayectory...

The equation ##x = x_0 + vt + at^2/2## is derived assuming a constant acceleration ##a##. My question is , from what frame is this path ##x(t)## described? Can I use it from a non inertial frame?

I state the following study and then expose my doubt at the end. MY SYSTEM A free particle (absence of forces) on one-dimensional space (X axis). INITIAL STATE At t=0 the wave function is a Gaussian wave packet NOT normalizet centered in ##x_{0}## and with standard deviation ##\sigma##...

Hi all, I am an electrical engineering student currently involved in a project aimed to create a simple GoTo azimuth mount. I don't have a lot of background in astronomy, so I am a bit confused on how to find the position of a star in the sky. After some research on my own, I figured out that...

A moving particle has been at position X for zero time. Was it ever at position X? Can zero time be considered as never, as in "I was in Rome for zero amount of time."? It seems like it would have been at position X if time passed in pieces the size of Plank time.

Homework Statement A charged particle has an electric field at ##\langle -0.13, 0.14, 0 \rangle## m is ##\langle 6.48\times10^3, -8.64\times10^3, 0 \rangle## N/C. The charged particle is -3nC. Where is the particle located? Homework Equations ##\vec E=\frac 1 {4π\varepsilon_0} \frac q {|\vec...

I'm currently in the process of applying for research positions in my field, unfortunately it's somewhat niche and research positions rarely become available. When they do they tend to go to those who they know already. So, I'm having to look at different research fields, which is kind of...

Hi! I would like to apply to a postdoc position, but one of the requirements is to detail at least a 2-page research plan on a certain topic. I haven't worked on that topic specifically before, so, I would need to research it. However, this may take sometime to know exactly what to do, and I...

I'm confused about something regarding phase shifts but I'm not sure I've pinned down what. I had always thought of a mirror as introducing a global phase shift of π in the position basis, but I only now realize that this makes no sense: of course -A ⊗ B = A ⊗ -B, so a global phase shift is not...

I started studying Lagrangian mechanics, and the movement equation is like this: d/dt (d/dz') L - d/dz L = 0 if the movement is on the z axis. Now the problem is, let's say L = M(z')2/2 - Mgz. How do we derivate an expression depending of z with respect to z' and also , an expression depending...

So I tried solving the differential equation for a spring - mass system using Euler's Algorithm in Python. The equation being d2x/dt2= -4π2x (The equation was obtained by Dimensional Analysis) here x and t are both dimensionless equivalents of position...

Homework Statement [see attached photo] I seek specific help with (a) only. The answers to this question are provided in the back of the textbook, so I know the answers (I hope). Homework Equations ##x(t)=Acos(\omega t+\phi _{0}),## ##v_{x}(t)=-A\omega sin(\omega t+\phi...

Homework Statement You throw baseballs at a mass rate of σ kg/s (assume a continuous rate) with speed u at the back of a car. They collide elastically with the car. The car starts at rest and has mass M. It moves on the ground with no friction. Find its speed and position as a function of time...