1d Definition and 383 Threads

Homework Statement The deuterium nucleus (a bound state of a proton and a neutron) has one bound state. The force acting between a proton and a neutron has a strong repulsive component of range 0.4 fm and an attractive component of range ~2.4 fm. The energy needed to separate the neutron from...

Homework Statement Solve the Laplace equation in one dimension (x, i.e. (∂^2h)/(∂x^2)= 0) Boundary conditions are as follows: h= 1m @ x=0m h= 13m @ x=10m For 0≤x≤5 K1= 6ms^-1 For 5≤x≤10 K2 = 3ms^-1 What is the head at x = 3, x = 5, and x = 8? What is the Darcy velocity...

In 3 space dimensions consider a 1D string under tension between two fixed points. Let the string lie at rest on the z axis between z = 0 and z = ∞. We can produce linearly polarized and circularly polarized waves if I move the end of the string properly? Now if we add an extra space dimension...

If a particle of mass moves in a One-Dimensional harmonic oscillating potential, and the particle is in the first excited state, what will it's wave function look like? And the significance of it being in the first excited state versus the ground state? Thanks for the input!

Hello, I have Navier stokes in 1D \rho\left(\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}\right)=-\frac{\partial p}{\partial x}+\mu\frac{\partial^2u}{\partial x^2} Condition of imcompressibility gives \frac{\partial u}{\partial x}=0 So I have Navier stokes...

Suppose we were to simulate 1D QED on a 1D lattice. How much information do we need at each lattice site given the mass, charge, and spin of the particles (does spin make sense in 1-1D spacetime?)? The links between lattice sites represent the gauge field? How much information is needed at...

In atom spectrum, such as for hydrogen, there are states of 1s, 2s, 2p, 3s, 3p, 3d, etc. There are no 1p, 1d or 2d, 2f. Simply because n= n_r + L +1. So the maximum of L is n-1. But when I read articles talk about meson, they list meson states of 1p, 1d, 1f, etc. Such as in the article “Quark...

My quantum text, leading up to the connection formulas for WKB and the Bohr-Sommerfeld quantization condition states that for \begin{align}u'' + c x^n u = 0 \end{align} one finds that one solution is \begin{align}u &= A \sqrt{\eta k} J_{\pm m}(\eta) \\ m &= \frac{1}{{n + 2}} \\ k^2 &=...

Ψ(x,t)=A⋅exp(A|x|)⋅exp(−iωt) Consider the one-dimensional, time-dependent wave function for infinite motion: (x,t) = Ae–a|x| e–it where A, a, and  are positive real constants. What are: (a) normalization constant A, (b) the quantum-mechanical expectation value of coordinate x...

Please help. My professor thinks I know this ****. Ψ(x,t)=Ae^-a(mx^2/η+it) A particle of mass m is in the infinite, one-dimensional, time-dependent state: where A and a are positive real constants. What are: (a) normalization constant A, (b) the potential energy function, U(x)...

Hi, There are three variables ax, ay and az, my question is: How to simplify the mean value <(ax^2+ay^2+az^2)^(1/2)> to <|ax|> ? What assumptions are required during the simplification? The statistical property of ax, ay and az is <ax^2>=<ay^2>=<az^2>. The assumption of the propability...

Expansion 1D Euler Eq.?? Trying to figure out an expansion step for 1D Euler Equations for unsteady gas flow. Continuity: \frac{\partial(\rho F)}{\partial t}+\frac{\partial (\rho uF)}{\partial x}=0 After Expansion: \frac{\partial(\rho)}{\partial t}+\frac{\partial (\rho u)}{\partial...

D'Alembert's solution to the wave equation is u(x,t) = \frac{1}{2}(\phi(x+ct) + \phi(x-ct)) + \frac{1}{2c}\int_{x-ct}^{x+ct} \psi(\xi)d\xi where \phi(x) = u(x,0) and \psi(x) = u_t (x,0). I'm trying to understand this intuitively. The first term I get: a function like f = 0 (x/=0), = a (x=0)...

Hello forum, I have a question regarding the delta function potential well. Given the following potential: V(x) = -αδ(x) for -a/2 < x < a/2 (α- positive constant) and V(x) = 0 elsewhere, how would one show that the ground state is the only eigenstate with E <0. One could of course solve the...

Short Version: It's been several years since I last practiced any mathematics or physics. I'm trying to get my mind as sharp as it was back then. I'm sure the solution is obvious, and just under my nose... I remember: P = P' + V't + (at^2)/2 Where P is position, P' is initial position, V'...

So I was sitting on the train last weekend, reading through my physics book on mechanical work and its relation to kinetic energy. One example would be that a box on a frictionless table being pushed and they would conclude that W = ΔK = ½mΔv2. Looking at this equation got me thinking...

Hi, I seem to have forgotten some of my math how-to, as I haven't done this in a while. Looking through my notes, Bird, Stewart and Lightfoot, Greenberg, etc. don't really help. My equation is this, at steady state: 0 = 1/r^2 ∂/∂r (D*r^2 ∂C/∂r) + P Where P is some production rate...

Homework Statement A rubber ball is shot straight up from the ground with speed vo. Simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest. At what height above the ground do the balls collide? Your answer will be a symbolic expressions in terms...

Hi. I want to write the entropy of a 1d harmonic oscillator as a function of energy, but for each energy there is only one possible configuration. So is the entropy zero? I mean, the energy is E=hw(n+1/2), so there is only one microstate for each energy.

I have a 1_D diffusion equation dc/dt = D*d^2c/dx^2-Lc where L,D = constants I am trying to solve the equation above by following b.c. by FTCS scheme -D*dc/dx = J0*delta(t); where delta(t)= dirac delta function ----(upper boundary) I have written the code for it but i just...

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 9.00 m/s. Find the location (above the base of the...

Hi! I have calculated various eigenstate wavefunctions for a one-dimensional system of a particle in a potential. The potential is an even function. All the wavefunctions have become either even or odd functions which I understand why. The ground-state wavefunction has always been even, is...

Hi, I have written a numerical code to solve the 1D heat equation in cyclindrical coordinates: \frac{\partial T}{\partial t}=\kappa\left(\frac{\partial^{2}T}{\partial r^{2}}+\frac{1}{r}\frac{\partial T}{\partial r}\right) The problem I'm considering is a hollow cylinder in an infinite...

Hello, consider a 1D elastic wave which have the amplitude: A=cos(x) What is the energy density: \frac{dE}{dx} of this wave? I seem to recall that the energy of a wave is proportional to the square of the amplitude: E \propto A^2 That seem to mean that \frac{dE}{dx} \propto cos(x)^2...

Homework Statement Given a square well, Infinite wall at x=0 Wall height U for x>L For E<U, find solutions to the schrondinger equation inside the well, and beyond x>L which satisy boundary conditions for x=0 and x=\infty Taking conditions at x=L, find the allowable energies of the...

Hi guys, I'm working through past papers and I have a problem with deriving the renormalised scaling of the following: [PLAIN]http://dl.dropbox.com/u/16658950/helpme.JPG I'm doing the rescaling as I would for a 1D ising model decimated with l = 2 (so every other spin, but N=4 in this...

Hello! I'm having the following problem; [PLAIN]http://www.hot.ee/jaaniussikesed/probleem_graafik.jpg I try to plot a 1D matrice with a sequence, or a 1D matrice and I get a result that "this value must be real". Now... what!? I am using MathCAD 14. Help is much appreciated, Uku

Homework Statement Consider phonons propagating on a one-dimensional chain of N identical atoms of mass M interacting by nearest-neighbour spring constants of magnitude C. Show that the Debye frequency can be written as w_{D}=\pi \left(\frac{C}{M}\right)^{1/2}. Homework Equations The...

Homework Statement Q: Two air track gliders of masses 300g, and 200g move towards each other in opposite directions with speeds of 50cm/s and 100cm/s respectively. Take the direction of the more massive glider as positive. If the collision is elastic, find the velocity of each glider AFTER...

I'm learning c++ and currently trying to write a little programme for 1D linear convection (wave equation). I have managed set all boundary and initial conditions as well as a mesh. But I have reached the point where I can't understand why the program does what it does. In red I...

I'm doing a project on a vibrating guitar string and I have completed all the simulation and experimental work, but I do not fully understand the theory behind it. I need to derive the 1 dimensional case of the wave equation, as the 1 dimensional case is considered to be the most convenient...

Homework Statement An infinitely deep one-dimensional potential well has a width of 1 nm and contains 10 electrons. The system of electrons has the minimum total energy possible. What is the least energy, in eV, a photon must have in order to excite a ground-state electron in this system to the...

Homework Statement A 50.0-g superball is traveling at 25.0 m/s bounces off a brick wall and rebounds at 22.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.50 ms (.0035 s) what is the magnitude of the average acceleration of the ball during this time...

Hey! I have some dumb-smart question Does 1D line have physical width? My logic says that mathematically you can go smaller and smaller,but I see there being a problem with 1D having infinitly small width in physics. If 2D object has infinitly many 1D lines that would suggest that 2D...

Homework Statement See figure attached for problem statement. Homework Equations The Attempt at a Solution Here's as far as I got, The part that confuses me is the range we should solve this equation. It says, \text{from } t=0 \text{ to } 1d I put the ^{-1} in...

Consider mass m_{1}and m_{2}with position vector (from an inertial frame) \overrightarrow{x_{1}} and \overrightarrow{x_{2}} respectively and distance between them be x_{0}. m_{1}\frac{d^{2}}{dt^{2}}\overrightarrow{x_{1}}=\overrightarrow{F} \Rightarrow...

All, I am reviewing for a comprehensive exam and am extremely weak on 1D Motion. Can you please help me out? A lab cart travels along the x-axis and its position as a function of time is given by the following expression: x(t)= 6m - (8 m/s)t + (1 m/s2)t2 1. Displacement of cart during time...

Homework Statement The question I have a one-dimensional linear spring with spring constant E. The tension is given by σ = Eε, epsilon = strain.. The left side of the spring is held fixed, the right side has a mass m attached to it. We can neglect gravity. What is the natural oscillation...

How would I come up with an equation (in one dimention), for the airy pattern of a telescope with a given diameter observing at a given wavelength? something that looks like this http://upload.wikimedia.org/wikipedia/commons/9/93/Airy_Pattern.svg I want to be able to plot Intensity in the...

Homework Statement Equation for a particle moving in one dimension with potential energy U(x): t=\int1/\sqrt{2(E-U(x))/m} , integrated from x0 to 5x0 Suppose U(x)=c/x for x>0. Calculate the time for the particle to move from x0 to 5x0, starting from rest at x0. Leave the answer in...

Homework Statement On June 14th, 2005, Asafa Powell of Jamaica set a world's record for the 100-m dash with a time t=9.77s. Assuming he reached his maximum speed in 3.00s, and then maintained that speed until the finish, estimate his acceleration during the first 3.00s. Homework Equations...

1. A parachustist jumps from an airplane and freely falls y=49.4 m before opening his parachute. Thereafter, he decelerates at a=2.02 m/s2. As he reaches the ground, his speed is 3.11 m/s. How long was the parachutist in the air? For this one I managed to get the solution already using a method...

Hello, I am trying to accurately simulate motion in 1D with a jerk that is changing non-linearly, but predictably. As an arbitrary example, picture jerk increasing logarithmically over time. This is being done in the context of a physics simulation that is 'stepping' frame-by-frame (ie 60...

Hi, I'm currently working through some exam papers from previous years before an upcoming module in Quantum Mechanics. Homework Statement See the attached image Homework Equations The Attempt at a Solution I'm a little stumped with this one, I'm assuming that I'm looking...

Hi, I'm currently working through some exam papers from previous years before an upcoming module in Quantum Mechanics. I'm a little stumped with this one, I'm assuming that I'm looking at a 1D harmonic Oscillator and the wording of the question suggests that the wave function just needs to be...

Homework Statement To save fuel, some truck drivers try to maintain a constant speed when possible. A truck traveling at 91.0 km/hr approaches a car stopped at the red light. When the truck is 115.7 meters from the car the light turns green and the car immediately begins to accelerate at...

Hi, I have the following problem. I am tried to numerically solve the 1D heat equation for a metal bar of length L. Using the forward time, centered space equation a(t+1) = a(t)+(alpha*deltaA/(deltaX)^2)*(a(x+1,t)-2*a(x,t)+a(x-1,t)) The problem is that I only have ONE heat source at...

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 5.85 m. The stones are thrown with the same speed of 8.59 m/s. Find the location (above the base of the...

Homework Statement An electron in a one dimensional crystal is bound by: U(x) = \frac{-\overline{h}^{2}x^{2}}{mL^{2}\left(L^{2}-x^{2}\right)} for \left|x\right| < L and x = infinity for \left|x\right| \geq L Show that a stationary state for the electron in the potential well \psi(x) =...

Let's suppose that we have two point particles with masses m1,m2 and the spherical shell with mass M, placed in a line, at distances h1,h2 and H from 0 in that line (0 is the center of some inertial frame of reference). The initial conditions and the equations of motion are the following...