1d Definition and 383 Threads

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...

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...

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...

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...

Problem 1 A commuter train travels between two downtown stations. Because the stations are only 1.00 km apart, the train never reaches its maximum possible cruising speed. During rush hour the engineer minimizes the travel interval Δt between the two stations by accelerating for a time interval...

Homework Statement In a historical movie, two knights on horseback start from rest 62 m apart and ride directly toward each other to do battle. Sir George's accleration has a magnitude of 0.21 m/s2, while Sir Alfred's has a magnitude of 0.26 m/s2. How far from Sir George's starting point do...

could anyone suggest the methods for solving the energy eigenvalues in a 1d finite potential well. are there any websites where we can directly get these instead of writing programs for rootfinding

Homework Statement Consider a particle confined in a 1D potential well of length L. Derive the normalized wavefunctions and energies of the eigenstates of the system in terms of the quantum number n, working from the time independent Schördinger equation. With the particle initially in the...

Hi all, I've been looking at the problem of two interacting electrons in a 1D infinite well and wanted to run my conclusions past other people to see if I'm on the right track. The potential is 0 from x=0 to x=1 and infinite outside of this. The 1 particle solutions to this potential are...

Homework Statement Hey, the question is about delta function potentials V(x) = -g[... del(x + 3b/2) + del(x + b/2) + del(x - b/2) ...] going on out to a large x in either direction. a) sketch the ground-state wave fn, write the form of psi(x) for -b/2 to + b/2 b) show that e^z =...

I have just started programming (started on C but currently using Ruby). This is literally my first proper program and I wanted some help and opinions. The problem is I am completely self taught using various random tutorials to learn the language and my own logic for the actual programs, so...

Problem Show that for a particle in a one-dimensional box, in an arbitrary state \psi(x,0), \langle E \rangle \ge E_1. Under what conditions does the equality maintain? Solution Note that any arbitrary particle in a one-dimensional box can be expanded in terms of the eigenstates \phi_n =...

Homework Statement a .450kg ice puck moving east with a speed of 3 m/s has a head on collision with a .9 kg puck initially at rest. Assuming a perfectly elastic collision what will be the speed and direction of each object after the collision? Homework Equations v1 +v1f = v2+v2f...

Hello: There is a well known theorem which asserts that every attractive 1D potential has at least one bound state; in addition, this theorem does not hold for the 2D or 3D cases. I've been looking for a proof in my textbooks on qm but I've been unable to find it. Can you help me out? Thanks!

Hello everyone. I have a question that i think belongs here or in the linear algebra section; but now i put it here, maybe someone will move the post if it's in the wrong place. The question: I have a normalized (1D) state in the x-axis in the harmonic oscillator...

I have trying solving this PDE for some random boundary values, and were wondering if someone could verify my calculations? \[ \begin{array}{l} T_t = DT_{xx} \\ T\left( {0,t} \right) = 0,T(\pi ,t) = 0,T(x,0) = \frac{1}{4}\left( {\left( {x - \frac{\pi }{2}} \right)^2 + \frac{{\pi ^2...

[SOLVED] Very beginner physics 1D motion question! Homework Statement Two cars move in opposite directions toward each other on a level, straight, one-lane road. When both drivers begin to brake, their front bumpers are 275 meters apart. The smaller car is initially moving at 25.0 m/s and the...

For a particle in a 1-dimensional box confined by 0<x<a. a)Construct a wave function phi(x)=psi(x,t=0) such that when an energy measurement is made on the particle in this state at t=0, the following energy values are obtained with the probabilities shown: Energy E_n Obtained ...

Ok, I have been given the steady state diffusion equation in 1d spherical polar coordinates as; D.1/(r^2).'partial'd/dr(r^2.'partial'dc/dr)=0 I know that the solution comes in the form c(r) = A+B/r where A and B are some constants. I just don't know how to get from here to there. I...

Homework Statement The solution to the diffusion equation in 1D may be written as follows: n'(x,t) = N/sqrt(4piDt) * exp(-x^2/4DT) where n'(x,t) is the concentration of the particles at position x at time t, N is the total number of particles and D is the diffusion coefficient. a)...

Hi all first post. Myself and my friends are very much stumped by this question. Any help would be much appreciated! Homework Statement A body with mass m collides directly with a body of mass 3m. If two thirds of the original kinetic energy is lost, find the coefficient of elasticity for...

I am in eleventh standard , In my book it is given about the plane progressive simple harmonic wave , later somewhere is mentioned about intensity of wave what my doubt is intensity is defined as energy/area but what about waves in 2d or 1d plane SHW are 1d as wave progresses in x-axis...

Hi all, I have another post on here relating to Fick's law of diffusion, but before I asked that I really should have started with this question: How do you go from a one dimensional version of the diffusion equation to a cylindrical co-ordinate system of the same equation? I have found...

Homework Statement The position of a particle moving along the x-axis depends on the time according to the equation x = ct2 - bt3, where x is in meters and t in seconds. For the following, let the numerical values of c and b be 3.5 and 1.0 respectively. (b) At what time does the...

Hi, I have a physics problem here that I'm quite stuck on. Maybe I'm making it harder than it seems: A ball is thrown upward with an initial speed, Vo. When it reaches the top of its flight, at a height h, a second ball is thrown at the same initial velocity. Find the height where the paths...

Hi. I have recently designed a simulator about Qunatum Mechanics one dimensional harmonic oscillator. Please try it. I will be glad to read your opinions. http://erham.persiangig.ir/Programs/1386/QM1DHOS10.png Size: 223 KB http://erham.persiangig.ir/Programs/1386/QM1DHOS10.zip"

Homework Statement particle in ground state of 1D harmonic oscillator - spring constant is doubled - what is the probability of finding the particle in the ground state of the new potential Homework Equations v=1/2kx^2 oscillator potential wavefunction ground state n=0 =...

Homework Statement A police car leaves in pursuit of a holdup car 0.50 h after the latter has left the scene of the crime at 120 km/h. How fast must the police car go if it is to catch up with the holdup car in 1.00h? Homework EquationsI'm thinking Vf=Vo+at? i must be wrong, I can't seem to...

FUN 1d motion prob--help Homework Statement The figure (http://img471.imageshack.us/my.php?image=picprobfd5.png) shows a general situation where a stream of people attempt to escape through a door that is closed. The people move toward the door at a speed of v = 3.50 m/s, are each d = .25 m...

For the well shown below (Attachment or Link belew) solve the time independent one dimensional Schrodinger equation for energies less than V0. You may (and should) leave your answer in terms of a single transcendental equation for the allowed wave numbers. \frac{-\hbar^2}{2m} ...

Homework Statement Two charges are on the X axis as follows: q1=3x10^-9 C at x=0.4metre and q2=5x10^-9 C at x=-0.2m. What is the size and direction of the sum of forces are on third charge q3=-2x10^-9 C at x=0? Homework Equations F=k|q1q2|/r^2 The Attempt at a Solution By my...

I have just started out with Physics, so please don't expect to much :) I've tried by myself to figure out where x = vt + ½t² comes from; I know (because I've read) how to deduce it from a v versus t graph, and that it only works with a constant acceleration. My question is as follows...

Homework Statement Two boats start together and race across a 42 km wide lake and back. Boat A goes across at 42 km/h and returns at 42 km/h. Boat B goes across at 21 km/h, and its crew, realizing how far behind it is getting, returns at 63 km/h. Turnaround times are negligible, and the boat...