1d Definition and 417 Threads

Homework Statement I have a charged particle in a 1D harmonic oscillator, on which an externally applied electric field acts, such that the Hamiltonian can be written: \frac{p^2}{2m}+\frac{kx^2}{2}-qEx The problem asks to first find the first (trivial) and second order corrections to...

I studied in AMO physics. nowaday, I study about BEC. I'm wonder, Difference between 1D lattice and 2D lattice on BEC. In the web, they just explain what they do using that. Maybe just short word, or sentence, give me a huge knowledge. Thanks you, and Have a nice day!

Homework Statement I believe this is a pretty standard question. A particle is initially in the ground state of a box of length L. Suddenly, the box expands symmetrically to twice its size, without disturbing the wavefunction. Show that the probability of finding the particle in the ground...

Homework Statement Find the eigenvalues and eigenfunctions of H\hat{} for a 1D harmonic oscillator system with V(x) = infinity for x<0, V(x) = 1/2kx^2 for x > or equal to 0. Homework Equations The Attempt at a Solution I think the hamiltonian is equal to the potential + kinetic...

Homework Statement Alright, well this is more of a math problem I guess... but here it is. \frac{\partial^{2}}{\partial x{2}} V = - \frac{I}{A\epsilon_o} \sqrt{\frac{m}{2e}} \frac{1}{\sqrt{V}} Everything besides the V is constant. Homework Equations Trying to solve for the potentialThe...

Homework Statement A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 76.0 m/s2 for 1.54 seconds, at which point its fuel abruptly runs out. Air resistance has no effect on its flight. What maximum altitude (above the ground)...

Homework Statement Problem taken from Cutnell & Johnson 8th Edition Textbook (though it's also in the 7th edition as well, can't recall question # though). It is from chapter 2, question # 10. In reaching her destination, a backpacker walks with an average velocity of 1.34 m/s, due west...

1. A stone is thrown with an initial velocity of +7.0 m/s. The acceleration of the stone is a constant and has the value of -9.81m/s^2.What is the velocity of the stone after 0.5s? 2. Homework Equations vf=vi+at? i have no idea 3. The Attempt at a Solution...

Homework Statement A jetliner leaves San Franciso for New york, 4600 km away. With a strong tailwind, its speed is 1100 km/hr. At the same time, a s2nd jet leaves New York for San Francisco. Flying into the wind, it makes only 700 km/hr. When and where do the two planes pass each other...

In reaching her destination, a backpacker walks with an average velocity of 1.31 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.54 m/s, due west, turns around, and hikes with an average velocity of 0.475 m/s, due east. How far east did...

Homework Statement A car traveling at a constant speed of 108 km/hr passes a trooper hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets in a chase after the car with a constant acceleration of 3.0 m/s2. How far does the trooper travel before he...

Homework Statement An object falls from height h from rest. If it travels .5h in the last second before hitting the ground, determine how long it takes to fall and the height h. xi = .5hm, t =1s, a = 9.8m/s^2, xf = 0m, Homework Equations Vf = Vi + at xf = xi + .5at^2 The Attempt at a...

Homework Statement The left ventricle of the heart accelerates blood from rest to a velocity of +26 cm/s. (a) if the displacement of the blood during acceleration is +2.0 cm, determine its acceleration (in cm/s^2). (b) How much time does blood take to reach its final velocity Homework...

Homework Statement A ball is launched vertically upward from ground level with initial speed of 20 m/s. 1. How long is the ball in air? 2. What is the greatest height reached by the ball. 3. How many seconds after launch is the ball 15m above the release point. (Air resistance is negligible)...

Homework Statement A batter hits a pop fly straight up. a) Is the acceleration of the ball on the way up different from its acceleration on the way down? (YES / NO) b) Is the acceleration of the ball at the top of its flight different from its acceleration just before it lands?Yes / No...

1D wave equation -- bizarre problem! I am trying to write a solver for a 1D wave equation in python, and I have run into a bizarre problem that I just can't find a way out of. I start with the wave equation, and then discretise it, to arrive at the following, phi(i,j+1) = deltat2/deltax2...

A sprinter running a 100 meter race starts at rest, accelerates at constant acceleration with magnitude A for 2 seconds, and then runs at constant speed until the end. a) Find the position (relative to the start position) and speed of the runner at the end of the 2 seconds in terms of A...

Hi there. Long time no see. I hope you're all well. Homework Statement An infinite 1D system has electron plane waves occupying states 0 <= E <= E_F. At time t=0, a potential step is introduced such that V=0 for x<0 and V=V' for x>0. What is the electron density when the system reaches...

Ok, so this example question is in my lecture notes: Homework Statement "For a 1-D quantum well, 5nm width, 2eV barrier height, calculate the number of energy levels in the well." Homework Equations So the equation given is a familiar one: E_n=\frac{n^2 \pi^2 \hbar^2}{2 m L^2}...

The physics of a 1D string with fixed end points is found here: http://www.uio.no/studier/emner/matnat/ifi/INF2340/v05/foiler/sim04.pdf Now imagine a string under tension T and of mass density rho confined to the surface of a cylinder of radius r. I posit that this string will act just as...

Homework Statement "Two non-interacting particles are placed in a one-dimensional harmonic oscillator potential. What are the degeneracies of the two lowest energy states of the system if the particles are a)identical spinless bosons b)identical spin-1/2 fermions? Homework Equations...

I am fairly new to QM and am learning many of the basics right now. We were just discussing conservation of operators (energy, momentum, etc) and I recalled a problem proposed in my textbook about a 1D particle in a box of length L. at a time t, the box suddenly expands to t=2L, in which time...

All are true false but need help on all of them thanks in advance 1)Knowing the position and velocity of a particle allows its future position to be predicted even if its acceleration is unknown. 2)Instaneous velocity is the derivative of the displacement time function. 3)If the...

My textbook simply states that "For a simple 1D walk with step size L: <x^2> = NL^2 So after N steps 99.7% of the particles will be closer then 3L sqrt(N) from the centre" How does it get from the first to the latter?

Hi all, I have studied the Landauer's formula from the book "Current at the Nanoscale", but a formula made me confused. In the general case, for a nanoscopic transport, the book gives the formula: http://img19.imageshack.us/img19/2986/33768834.jpg In the following paragragraph it is...

Homework Statement I need to find the mean square distance between the 2 particles. Before I can do that, I need the expectation of x_1^2 and x_2^2 , then x_1x_2. I an on the first part and got stuck.Homework Equations <X_1^2>=\int_0^L \int_0^L x_1^2 |\psi_{n,m}(x_1,x_2)|^2 dx_1dx_2 where...

Homework Statement A particle of mass m is in a one-dimensional infinite square well that extends from x = –a to x = a. a) Find the energy eigenfunctions ψn (x) and corresponding eigenvalues En of this particle. (Hint: you may use the results of the book for an infinite square...

Homework Statement We addrewss a one dimensional system. An atom moves along the x-axis with a kinetic energy K = 0.5*m*v**2. In the range -x0<x<x0 the atom enters the trap, and is affected by a magnetic fiels. The interaction with the magnetic field gives rise to a potential U(x) which we...

1. Quantum well structure can be realized by sandwiching layers of semiconductor and two insulators. This sandwiching problem was often treated with 1 D infinite well. Suppose now the problem is 3 dimensional well with length L at z direction from 0 to L, at which V(x,y,z)= 0 when 0<z<L...

Homework Statement An electron is confined to the region of the x-axis between x = 0 and x = L (where L = 1nm). Given a state n = 3, find the location of the points in the box at which the probability of finding the electron is half it's maximum value Homework Equations...

Hello, This is the first time I'm using COMSOL on a problem where I have multiple subdomains within the domain. Previously, I have only been using one domain/one set of equations/Two global sets of BC's. I've been having a hard time thinking of a solution to my problem. I have 3...

Hey there! I'm faced with this problem: http://img7.imageshack.us/img7/4381/25686658nz9.png It's a 1D nonhomogeneous wave equation with a "right hand side" equaling to the dirac delta function in x * a sinusoidal function in t. I have to find its general solution with the constraints...

Homework Statement A tortoise can run with a speed of 0.10 m/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 5.0 minutes. The tortoise wins by a shell (40 cm). (a) How long does the race take? (s) (b) What is the length of...

Hi all, My maths are very rusty and I would need some advice. I have some experimental results obtained in an open channel and got depth-averaged velocity u(y) at different cross-sectional locations y. I tried different models but there is one I don't know how to tackle. The following one...

Problem:IF there is heat radiation within the rod of length L , then the 1 dimensional heat equation might take the form u_t = ku_xx + F(x,t) Find u(x) if F = x , k = 1 , , u(0)=0 , u(L) = 0 the problem is that i am not sure what this is asking me , how can i find u(x) if i have...

Homework Statement A ball is dropped from the top of a 50.0 rm m-high cliff. At the same time, a carefully aimed stone is thrown straight up from the bottom of the cliff with a speed of 21.0 m/s. The stone and ball collide part way up. Homework Equations v = v0+at x = x0 + v0t +...

Hi, I am wondering what is the difference between 1D spectra and 2D spectra? I see many documents talking about one of these 2, but I couldn't find any clear definition...

In the text, there is a rubber band model for 1D chain of N links. Assume each link of the rubber band is align horizontally either to the right or to the left. In the text, define N_+ as the number of links directed to the right and N_- represents the number of links directed to the left. I...

Hi all, I'm wanting to write a small program simulating a 1D lattice with some motion. I have the equation: m_{n}\frac{d^{2}u_{n}}{dt^{2}}= k_{n,n+1}(u_{n+1}-u_{n})+k_{n-1,n}(u_{n-1}-u_{n}) Then using a simple trial plane wave (u_{n}=Ae^{-i\omega t}). It boils down to: - \omega^{2}...

For 1D well with size a, the potential is V and when 0<=x<=a, V=0; othersize V = infinity the Schrodinger equation becomes \frac{d^2 f}{dx^2} + k^2 f = 0 where f is the wavefunction. For solving the equation, many textbook choose f = A\sin(kx) + B\cos(kx) as the...

Homework Statement A 2kg object moving 5m/s in the positive x direction has a one dimensional elastic collision with a 4kg object moving at 1m/s in the same direction. What is the resulting change in kinetic energy of the 4 kg object? Homework Equations K=1/2 m*v^2 m1v1+m2v2=(m1+m2)V...

Homework Statement A particle is inside of a potential described by: H = p^2/2m + 1/2kx^2, x between -L/2 and L/2 H = infinity, otherwise. my task is to compute a first-order approximation to the energies of this potential. The Attempt at a Solution I attempted to use...

Homework Statement Homework Equations The Attempt at a Solution As a group we're stuck on this as a result of the lecturer saying that he wouldn't help us because we should work as a group and find other ways other than asking him about it. Which is fair enough - but none of us...

1. Solve the one dimensional heat equation for a rod of length 1 with the following boundary and initial conditions: BC: \partialu(0,t)/\partialt = 0 \partialu(1,t)/\partialt = 0 these are the wrong boundary conditions (see below) Actual BC: \partialu(0,t)/\partialx = 0...

A block of mass m1 = 1.0 kg slides along a frictionless table with a velocity of +10 m/s. Directly in front of it, and moving with a velocity of +3.0 m/s, is a block of mass m2 = 9.0 kg. A massless spring with spring constant k = 1120 N/m is attached to the second block as in the figure below...

1. A ball is dropped of the top of a building whose height is d. The ball falls the last 2/3 of its distance in 3 seconds. What is the total time of its fall? What is the total distance of its fall? I used this equation to start this problem...

A suspicious-looking man runs as fast as he can along a moving sidewalk from one end to the other, taking 2.50 s. Then security agents appear and the man runs as fast as he can back along the sidewalk to his starting point, taking 8.00 s. What is the ratio of the man's running speed to the...

Just wondering is the solution right?it is a 1D kinematic problem Homework Statement An elevator ascends with an upward acceleration of 1.2m/s^2. At the instant its upward speed is 2.4 m/s, a loose bolt drops from the ceiling of the elevator 2.7m from the floor. Calculate the time of flight...

Hello everyone. I am stumped here with this problem, i feel like it should be fairly simple but i can't seem to figure it out. Homework Statement If the acceleration for a given object is given by the function: a(t) = +(3 m/s^3) · t (Note: units are included in the eqn, so if [t]=s...

1. The problem statement I am studying for an upcoming test and I am having a lot of trouble relating velocity, acceleration, and displacement vs time. Given a position vs time function: x(t) = 6m - (8m/s)t + (1m/s^2)t^2 I cannot for the life of me understand how to find any instantaneous...