1d Definition and 417 Threads

I want to solve the Schrodinger via the Numerov Method but I had some troubles. I'm programing in C++, so here is my code: #include<cstdlib> #include<iostream> #include<cmath> using namespace std; double x_min=-4.0 , x_max=4.0; int N=2000; double...

Hello, What does it means when a particle having mass "m" in a one dimensional potential well has the potential given by: V(x)= \stackrel{-\alpha δ(x) for |x|<a}{∞ for |x|≥a} where δ(x) is the delta function and \alpha is a constant. I understand that the well boundries have...

Homework Statement A system is made of N 1D simple harmonic oscillators. Show that the number of states with total energy E is given by \Omega(E) = \frac{(M+N-1)!}{(M!)(N-1)!} Homework Equations Each particle has energy ε = \overline{h}\omega(n + \frac{1}{2}), n = 0, 1 Total energy is...

Hey guys, I'm new to this forum and was hoping to get a clear answer regarding the difference between 1D, 2D and 3D flows in hydraulics (ex. 2D Numerical Model...) ? Thanks a bunch! -A.

Hi all, I have the question: Consider a flag blowing in the wind. Assume the transverse wave propagating along the flag is one dimensional. Solve the wave equation for the wave on the flag, assuming the displacement of the flag is zero at the flag pole and the other end of the flag is...

Homework Statement Derive from Maxwell's equations these Hill equations for 's' and 'p' mode waves; s\hspace{3mm} modes: E(r,t) = \Psi_{s}(z)e^{i(\beta x - \omega t)}y \\ \hspace{10mm}Hill\, Equation for\, \Psi_{s}(z)\\ \hspace{17mm} \dfrac{d^{2}\Psi_{s}(z)}{dz^{2}} +...

Homework Statement Prove that, for any 1D elastic collision between two particles: as viewed from the centre of mass (or zero momentum) frame of reference, the velocity of each particle after the collision has the same magnitude but opposite sign to its velocity before the collision. 2. The...

Homework Statement I have a system of N non-interacting anharmonic oscillators whose potential energy is given by, V(q) = cq^2 -gq^3 -fq^4 where c,f,g > 0 and f,g are small. Homework Equations The Hamiltonian is given by, H = \sum_{i=1}^N \big ( \frac{p^2_i}{2m} + V(q_i) \big )...

Homework Statement Consider a one-dimensional quantum system described by the potential: $$V(x) = -V_o + \frac{1}{2}mw^2x^2\,\,,V_o > 0\,\,\text{for}\,\, |x| < b\,\,\text{and}\,\,0\,\,\text{otherwise}$$ Show that the state described by: $$\psi_{-}(x) = R_{-}...

Homework Statement The generalization of the bohr rule to periodic motion more general than circular orbit states that: ∫p.dr = nh = 2∏nh(bar). the integral is a closed line integral and the "p" and "r" are vectors Using the generalized rule (the integral above), show that the spectrum for...

Homework Statement Two stones are thrown simultaneously, one straight upward from the base of a cliff and the other straight downward from the top of the cliff. The height of the cliff is 6.00m. The stones are thrown with the same speed of 9.0m/s. Find the location (above the base of the cliff)...

Appendix 1 - simple Lorentz transformation derivation found at - http://www.bartleby.com/173/a1.html Given in equation (3) (x'-ct') = Y(x-ct) [Y = const.] by rearrangement, it yields, (x'-ct')/(x-ct) = Y. But it is stated that both (x-ct) and (x'-ct') are zero, so...

Homework Statement 1)A ball is dropped from the top of a 56.0 m-tall building. After 2.00 s, another ball is thrown upward from the ground. When the two balls pass the same point, they have the same speed. How fast was the upward-bound ball thrown? 2)You are riding an elevator with an...

Suppose a particle is moving along the $x$ axis with velocity $v$. It starts at the point $-5$ and has constant negative acceleration $a$. You need to find what time the particle reaches the origin. My teacher solved this question, and used the kinematics equation Δx = v_0t+1/2 at^2...

Hi all, I am studyng the "ding-a-ling" model for the Heat transfer in a 1D chain. Particularly, from this article: http://polymer.chph.ras.ru/asavin/teplopr/mb97pre.pdf I need help with the equation (1), I don't know specifically what the "hard-point core" interaction means. I was thinking...

Morning all, This is probably going to seem absurdly simple, however I need to do a very quick conduction calculation as part of a much larger problem I am working on. I was wondering if anyone would be able to give me some pointers as time is of the essence. The scenario can be simplified as...

Homework Statement I am designing a physics simulation that models two balls colliding along a straight line path. I can change the coefficient of restitution, the initial velocities, and their masses. THe assignment asks that we vary at least three parameters, so in my case, the three are...

Homework Statement This is from Kleppner, problem 1.12 in the 2010 edition, if you want to see the diagram. The acceleration of gravity can be measured by projecting a body upward and measuring the time that it takes to pass two given points in both directions. Show that if the time the...

Hi. Since these equations are approaching three hundred years old I'm pretty sure someone must have solved them somewhere before. However I have not been able to find any text-books or papers that actually show me how to solve these equations. So I'm wondering if anyone here know where I can...

Say I have a model, y = f(x), and ten discrete data points to compare to this model, (x1, y1)...(x10,y10). The normal way would then be to take the residuals and square them to get a quality of fit, ie. average residuals squared = {[f(x1) - y1]^2 + ... + [f(x10) - y10]^2}/10 I also remember...

1. A given string length L, connected at one end while the other end is free. Assume that the string moves in one dimensional, ie, the amplitude can be described by a function of the shape of his y (x, t). What is the average kinetic energy (as a string), assuming it moves with the lowest...

I use transfer matrix method. I try to plot the phase Φ(ω) versus frequency ω graph in the vicinity of a band gap. The transmission coefficient t(ω) is t(ω) = |t(ω)|*exp(i*Φ(ω)) from which I get the transmission phase Φ(ω) = atan(t_imaginary(ω)/t_real(ω)). Since I assume that -pi/2 ≦ Φ ≦...

Is there some mathematical prove that for ground state in QM problems wave function doesn't have any zeros?

I am dealing with a set of data where I have values C(x,t) for a discrete set of x and t values. Say: x={1,5} t={1,3,7} C={{C(1,1),C(1,3),C(1,7)},{C(5,1),C(5,3),C(5,7)}}. How do I combine this to a list that looks like...

Homework Statement A 55 kg woman jumps to the floor from a height of 1.5 m. If her body comes to rest during a time interval of 8.00 * 10^-3 seconds, what is the force of the floor on her feet? Homework Equations Unit conversion and g = 9.8m.s^2 ~ 10 m/s^2 The Attempt at a...

1D solid, 0<x<L, with the following boundary conditions: The whole solid is at T = T1 at t=0. x = 0 is held constant at initial temperature T1 for all t. There is a constant flow of heat, dQ/dt out of the solid at x = L. T(0,t) = T1, T(L,0) = T1, How do we go about solving the heat equation...

Hi all, According to quantum theory, for an electron vibrating in one dimension, only probability of position is meaningful. My question is will there be a e&m radiation by such a motion, if yes, how to appreciate it from the possibility argument, say, if only the probability at each position...

Homework Statement (i) Write an expression for the wave function of 2 particles in a 1D box. Assume that their masses are the same, m, and that the box size is a = 1. What are the energy states? (Comment: The particles are distinguishable) (ii) Write an expression for the average distance...

Homework Statement Sorry if this should be in intro section. I'm not sure the math required. So I have \frac{d^2\psi}{dx^2}=-\frac{2mE}{\hbar^2}\psi I would like to see how I can get the solution that my book gives me which I know is \psi(x)=A\sin kx+B\cos kx where A and B are...

Homework Statement Show that the following is an eigenfunction of \hat{H}_{QHO} and hence find the corresponding eigenvalue: u(q)=A (1-2q^2) e^\frac{-q^2} {2} Homework Equations Hamiltonian for 1D QHO of mass m \hat{H}_{QHO} = \frac{\hat{p}^2}{2m} + \frac{1}{2} m \omega^2 x^2...

Homework Statement 2 objects A and B. A has a 4000 m. head start on x-axis heading to the right Va = 50 m/s; Vb = 55 m/s aa = 0.5 m/s2 ab = 1.0 m/s2 need to know t in s when xa = xb Homework Equations r = r0+vt-a(t2/2) The Attempt at a Solution I set each up for xa,b in...

Homework Statement basket ball player throws a ball up in the air and the ball travels 3.2meters before stopping. if the basketball player jumps .5 seconds after throwing the ball. what velocity does he need to reach the ball. Homework Equations vf^2=v1^2+2as sf=si+vot+1/2at^2 vf=vi+aot...

1. The distance from two airports is 1286 km by air. Plane A leaves the first airport at 10:00a heading north toward the second airport, another plane leaves from the second airport at 11:00a heading south towards the destination plane A originally departed from. Plane A travels at 720km/h, and...

Homework Statement I have a question: what's the relationship between the probability of finding the particle and the particle's energy? if x is the same. Homework Equations The Attempt at a Solution the first question i had 30% for ground state 2nd energy level i got 2% 3rd...

Hey I have a question pictured below: I always seem to struggle with questions like these, my understanding is we know the spacing of K-states throughout the lattice is given by \frac{2\pi}{L} Such that the fermi wavevector divided by this spacing and multiplied by 2 due to the fact...

Have been trying for hours but simply no results. Hope that someone can help me out. \[\frac{\partial u}{\partial t}=4\frac{\partial^2 u}{\partial x^2}\] for \(t>0\) and \(0\leq x\leq 2\) subject to the boundary conditions \[u_x (0,t) = 0\mbox{ and }u(2,t) = 0\] and the initial condition...

Homework Statement I'm implementing the transfer matrix method (manually) for an EM wave through a 1D layered structure. Basically I'm just considering a plane wave in the positive-x direction, conserving E and H across each material interface, and constructing interface matrices, the...

Homework Statement An object with total mass mtotal = 8.6 kg is sitting at rest when it explodes into two pieces. The two pieces, after the explosion, have masses of m and 3m. During the explosion, the pieces are given a total energy of E = 48.0 J. 1) What is the speed of the smaller piece...

I'm looking for the analytical solution for the 1D convection diffusion equation with a constant heat flux. Boundary conditions: The domain I'm looking at is x from 0 meters to 1 meter. The temperature at x=0 is T=0 degrees Celsius. At x=1, T=100 C. I'm given the equation...

Given The 1D wave equations p_{x}'' - (1/c_{0}^2)p_{t}'' = 0 u_{x}'' - (1/c_{0}^2)u_{t}'' = 0 ρ_{x}'' - (1/c_{0}^2)ρ_{t}'' = 0 and linearised continuity and momentum equations ρ_{t}' = -ρ_{0}u_{x}', ρ_{0}u_{t}'=-p_{x} how may one derive the following two equations? u=p/ρ_{0}c_{0}...

I am trying to model a thermal mass for a greenhouse design. A thermal mass is basically a box of mass with high Cp buried in the ground with the top exposed to the inside of the greenhouse and all the other sides insulated. My model is based on the fact that during the day, there is a net...

Homework Statement A quantum particle is free to move in a infinite 1d potential well of length L excited on the second excited state n=3.What is the probability to locate the particle between 0 and L/3. Homework Equations ∫ψ^2=1 ψ=sqrt(2/L)sin(n∏x/L) The Attempt at a Solution...

Homework Statement 5. An object is thrown vertically upwards with a speed of 72 kilometres per hour. How long does it take to reach a point 25 meters below the starting point? You can take g as 10 ms-2 for convenience. Here is my answer. I got 4 yet the answer is 5...

http://imageshack.us/a/img824/1121/asdasdaw.png I am having trouble completely understanding what the question wants. I know it is quite clear but the part I am having trouble is the following. It says 'pretend' w(x,t) is a solution to the 2D equation, just independent of y, then to...

I was studying a book on QM and found out that the wave function for a free particle of completely undetermined position traveling in positive x direction is given by e^(2(pi)i(kx - nt)) where n is the frequency i have been trying a lot to derive it but till now i can't . Can anyone help me

Homework Statement Consider the 1D potential V(x) such that V(x)=0 for x<0 and V(x) = V for x>0 and assume that a wave packet with energy E0=p20/2m<V is incident on the barrier from the left. Calculate in terms of E0 and V the difference in time between the arrival of the incident packet at...

Homework Statement A mosquito flies toward you with a velocity of 2.2 km/h (E). If you are traveling toward the mosquito with a speed of 1.9 m/s, and a distance of 21.0 m separates you and the mosquito initially: A) What will your displacement be when you hit the mosquito? (7) B) How long...

Bear with me (Two part question), In the ideal case, an electron in a lattice under the influece of a static force will undergo bloch oscillations. A simple hamiltonian for this system would be: H=H° +Fx and V(x+d)=V(x) If I used the kronig-Penney Model would I be able to derive...

1D Dynamics Problem! Homework Statement A car of mass 1100kg is traveling at a constant velocity of 60 km/hr, east. The coefficient of friction between the tires and the road is 0.45. The driver of the car sees the traffic light in front turning red and steps on the brake, only to find that...

Trying to create a table with time and instantaneous velocity. (the tables- http://i.imgur.com/8DZsu.png ) How do I go from using the Average Velocity to the Instantaneous Velocity? Instantaneous Velocity is the V_avg at t_1 + (delta-t)/2 how do I use this with my data.