Position Definition and 1000 Threads

Homework Statement Given the following k-space representation of the wave function: Ψ(k,t) = Ψ(k)e-iħk2t/2m use the wave number representation to show the following: <x>t=<x>0 + <p>0t/m <p>t=<p>0 Homework Equations <x>=∫Ψ*(x,t)xΨ(x,t)dx <p>=∫Ψ*(x,t)(-iħ ∂/∂x)Ψ(x,t)dx The Attempt at a...

Homework Statement At what time in the future will the x-component of the masses position be at 0m? Homework Equations x=x,initial+(integral0,t)(v,xcomponent)(dt) The Attempt at a Solution The solution is 3.1 seconds... not really sure where to start :(

Homework Statement The problem is hopefully attached, I had to take a screen shot. Homework Equations I understand the process of taking the derivative of position to get velocity. *refer to derivative rules... for example r(x)=2x^2-6x+8 therefore r`(x)=4x-6 The Attempt at a Solution I am...

Homework Statement A car sits in an entrance ramp to a freeway, waiting for a break in the traffic. The driver sees a small gap between a van and an 18-wheel truck and accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line...

Hi, I have a question about where's the most efficient place for a train engine - Let's say a train has to do a some route back and forth, the route has curves and positive and negative slopes. In real life - What's the best position for the enginge? My intuition says it will be most efficient...

Suppose i have a random variable X and its standard deviation dx. We could write the average with error like $$<X>\pm dx/2$$. But how do we know it is centered or not ? It could be +1/4 -3/4 for example.

Homework Statement Please see the attachment for a better picture The energy of an electron in a hydrogen atom is: E = p^2/2m - αe2/r; where p is the momentum, r the orbital radius, me the electron mass, e the electron charge, and α the Coulomb constant. Use the uncertainty principle for...

What does it mean by "In the position representation -- in which r is diagonal" in the paragraph below? How can we show that? Does it mean equation (3) in http://scienceworld.wolfram.com/physics/PositionOperator.html? (where I believe the matrix is in the ##|E_n>## basis)

While discussing the anatomy of the female reproductive system someone brought a question about the position of the ovary. The question was the ovary is closer to which part of the Fallopian tube? The answer looks pretty obvious. We thought it should be the infundibulum as actually it's...

Hi guys, I got one confusion when reading Goldstein's Classical Mechanics (page 20, third edition). After getting the equation, then it says that Note that in a system of Cartesian coordinates the partial derivative of T with respect to qj vanishes. Thus, speaking in the language of...

I am following Griffiths' intro to quantum mechanics and struggling(already) on page 16. When a particle is in state ##\Psi##, $$\frac{d<x>}{dt} = \frac{i\hbar}{2m}\int_{-\infty}^{\infty} x\frac{\partial}{\partial t}\bigg (\Psi^*\frac{\partial \Psi}{\partial x}-\frac{\partial \Psi^*}{\partial...

in shm,if minimum potential energy of an shm is not zero,does that mean that in mean position ,spring is stretched. eg mass attached to a vertical spring.

Homework Statement Three blocks of identical mass are placed on a frictionless table as shown. The center block is at rest, whereas the other two blocks are moving directly towards it at identical speeds v. The center block is initially closer to the left block than the right one. All motion...

Hi everyone. So I have been learning about equilibrium recently in class... and suppose I have the following reaction: A(s) + B(aq) <-----> C(aq) + D(g) [Note: in parentheses, I indicate the state of my substances] So I was told recently that pulverizing my solid "A" would not change the...

The torque is the cross product with a position vector (that is the lever lenght) and a force But i the is torque also if there isn't a lever? I mean an instantaneus torque that is different in each point we consider it like in the photo It is also a torque even if something doesn't rotate...

Homework Statement The acceleration of a particle moving only on a horizontal xy plane is given by a = 3ti + 4tj, where a is in meters per second squared and t is in seconds. At t = 0, the position vector r = (20.0 m)i + (40.0 m)j locates the particle, which then has the velocity vector v =...

Homework Statement Homework Equations Relevant equations can be derived from the formulas, by exchanging x to v, v to a, etc. The Attempt at a Solution I've tried to graph them, but I am not able to visualize or understand them. Please help me about these questions, I need some hints. If...

Homework Statement Consider a particle, with mass m, charge q, moving in a uniform e-field with magnitude E and direction X_1. The Hamiltonian is (where X, P, and X_1 are operators): The initial expectation of position and momentum are <X(0)> = 0 and <P(0)>=0 Calculate the expectation...

1. Problem Statement Assume there is an rigid object with mass m in 2D space, an impulse J = FΔt is applied at time t1 at the particle Pimp and Pimp is on the exterior boundary of the object. The impulse cause a free plane motion of the object and the object is only affected by the force of the...

Hi all, This is the problem I want to share with you. We have the hamiltonian H=aP+bm, which we are commuting with the position x and take: [x,H]=ia, (ħ=1) Ok. Now if we take, instead of x, the operator X=Π+ x Π+ +Π-xΠ- where Π± projects on states of positive or negative energy the...

Homework Statement Between t = 0 seconds to t = 2 seconds the velocity is 3 m/s ihat. Between t = 2 seconds and t = 6 seconds the velocity is -2 m/s ihat. I need to know what the position is at each second. Homework Equations Position = velocity * dt The Attempt at a Solution I know that the...

Can't see where I'm going wrong here - would greatly appreciate if anyone can point it out! I've gotten the other parts of the question right, so I know that: ω = 125.66 rad/s A = 2.50 * 10-3m k = 3.49 rad/m The wave is moving in the +x direction. The general equation for the position of a...

Hi. Hoping for some help with the following questions - 1 - Are there any momentum eigenstates in a box ? I think the answer is no because if i solve the momentum eigenvalue equation in 1-D i get Aikx but it seems impossible to get this to meet the boundary conditions 2 - As far as I know a...

Homework Statement Problem: how do we know for sure if x is <0 for point A? Vx-t is a graph of particle's speed over time. x represents position of the particle at any given time The Attempt at a Solution From the function that we can see on the left side of the picture we can deduce the...

Homework Statement A piston-cylinder device attached below is shown in Figure 6.A-31where Patm = 100 kPa Tamb = 150°C piston Ac = 0.01m2 mp = 100 kg water T1 = 350°C P1 = 400 kPa z1 = 0.5m Figure 6.A-31: Piston-cylinder device. The initial position of the piston is z1 = 0.5 m and the piston...

Following a cold or flu I'm often afflicted by a persistent cough which keeps me awake at night. After a recent bout of the flu I discovered that sleeping in the "recovery position" allowed me to easily make it through the night with little or no coughing. If I did not maintain the position...

Homework Statement Two particles are separated by a distance d, Particle A has charge +Q and Particle B has charge +3Q. At what distance from particle A along the line connecting particles A and B would you place a third charged particle such that no net electrostatic force acts on it ...

Homework Statement Homework Equations Xcm = (x1m1+x2m2) / (m1+m2) The Attempt at a Solution ok so I'm having trouble understanding what's happening in the question... when the penguin moves, is the sled also moving? If it's friction less ice then if the penguins moves L, the sled will...

Why almost every crystal system has peak around 32 degree (2 theta) ?

My goal is to fight the max amount of torque with the weight by having different densities at different places and by keeping the z center of mass low. I need to find the answer out in terms of the three angles, and the final answer must not have a substituted angles such as 45 degrees. I need...

Homework Statement An opaque card is pierced by two small holes 4 mm apart and strongly illuminated from one side. A lens on the other side of the card focuses images of the holes, 16 mm apart, on a screen 125 cm from the card. Find: (a) the position of the lens, (bc) the focal length. Why are...

I want to have three plot 1,2,3 in Matlab with the symbols (a), (b) and (c) on plots 1, 2 and 3 respectively.I can do it by text('(a)'), text('(b)'), text('(c)') on the plot 1,2 and 3 respectively but I want to have the three symbols on the same position on the three plots for example...

Homework Statement What would the slope of a position vs time squared graph represent?Homework Equations X=my^2+bThe Attempt at a Solution I thought the slope of this graph would be velocity due to the fact that the normal position vs time graph slopes are velocity. However, I was told that the...

Homework Statement Hi! I just found this forum after trying to calculate something regarding a satellite's orbit. Hope that you can help me here. So, I need to calculate the matrix of a satellite's site vectors. I have found it in the ECEF form, but since the satellite is doing observations in...

Hello, In this simulation (link is below) the graph of the potential energy with respect to position U(x) when there is no friction on the ramp looks like the graph of potential energy of Hooke's Law spring U(x)=(1/2)KX^2). For the spring, the negative of the derivative is equal to the...

I attached the info that I need help with I am really struggling and the lines that are drawn in red are my guesses. PLEASE HELP!

I am currently in the honors mathematics program at my school. I wanted to get a research position this summer with a professor. I have been reading some of the previous threads about people asking for the same type of advice that I am asking for. I just feel that my situation may be a bit...

Homework Statement Given the following graph of displacement vs time for an object moving in a straight line (assume const accel): Find the acceleration between t=0 and t=4 Homework Equations A= ((vi-vf)/2)/time The Attempt at a Solution I've tried find the area of t=0 to t=4 in order to...

Current situation: -$60,000/year salary - 10 days vacation + 5 sick/personal days - Health, Dental, Eye insurance What i like about my current job: Camaraderie with other developers If i have a question i usually have more than one person i can ask Currently on the most important project +...

Hi! A friend of mine is interested in a PhD position in a Scandinavian country. There are no specific calls for projects, but the group webpage mentions available positions and encourages anyone that is interested to send an email for information. A formal application obviously comes later, so...

Homework Statement A cannon with muzzle speed of 1000m/s is used to start an avalanche on a mountain slope. The target is 2000m horizontally from the cannon and 800m above the cannon. At what angle above the horizontal should the cannon be fired. Homework EquationsThe Attempt at a Solution I...

Hi, I wish to get position operator in momentum space using Fourier transformation, if I simply start from here, $$ <x>=\int_{-\infty}^{\infty} dx \Psi^* x \Psi $$ I could do the same with the momentum operator, because I had a derivative acting on |psi there, but in this case, How may I get...

Hello, I need to create a 2-D electron energy density plot in Mathematica to compare with my STM experimental results in my lab class. This would be done by plotting the superposition of the symmetric and anti-symmetric wave functions, $$\Psi_s(\textbf{r}) =...

Homework Statement Q: The position of a dragonfly that is flying parallel to the ground is given as a function of time by r⃗ =[2.90m+(0.0900m/s2)t^2]i^− (0.0150m/s3)t^3j^ . At what value of t does the velocity vector of the insect make an angle of 30.0 ∘ clockwise from the x-axis? . Homework...

Homework Statement Someone runs on a circle in the direction of a clock. He goes at constant speed. The circle is put in a xy plane that is centered at the origin. The radius is 10 m. At a certain moment he has a speed of (3i + 3j) m/s. Determine the position at this moment. (in vectorial...

As shown in Figure Q1a, a frictionless, massless, piston, supported by two springs, A and B, is held by a pin in a vacuum inside a rigid-walled container. The properties of the springs are: spring constants kA = 3,859 and kB = 3,090 (in N/m), natural lengths LA0 = 0.03 and LB0 = 0.1 (in m). When...

As shown in Figure Q1a, a frictionless, massless, piston, supported by two springs, A and B, is held by a pin in a vacuum inside a rigid-walled container. The properties of the springs are: spring constants kA = 3,859 and kB = 3,090 (in N/m), natural lengths LA0 = 0.03 and LB0 = 0.1 (in m). When...

Homework Statement Find tangent line of y=xe^{\frac{1}{x}} at point x=\alpha and it's limit position when \alpha \rightarrow +\infty. Homework Equations Tangent of y=f(x) at point M(x_0,f(x_0)): y-y_0=f^{'}(x_0)(x-x_0) The Attempt at a Solution Applying the above equation for tangent of...

Homework Statement The diagram shows the impact of 20 projectiles launched at the same speed and angle. What is the uncertainty in the impact position? (see attached file for picture of diagram) Homework Equations No equations, my lab instructor said through an email that I can get it "just by...

Homework Statement This is for a junior level classical mechanics course. We're currently working with Newton's Laws. A particle of mass m moves under the influence of a force ##\vec{F}(t,v)=-ktv \hat{v}##, where k is a positive constant. At time t=0, ##v=v_0 \hat{x}## at the origin, where...