1d Definition and 419 Threads

Homework Statement There's a particle moving in a 1D potential V(x) with mass m. The particle's normalised wavefunction is ψ(x,t). Use the time dependent Schrodinger equation to show that ##\frac{\partial{\rho}}{\partial{t}} + \frac{\partial{j}}{\partial{x}} = 0## Where ##j(x,t) =...

Hi all, I've been self-studying a first year uni introductory mechanics course, and I'm confused with the derivations involved in calculating the final state of an elastic collision in one dimension, given the initial state. So basically we have masses of m_1, m_2 with initial velocities v_1i...

Homework Statement [/B] During your summer internship for an aerospace company, you are asked to design a small research rocket. The rocket is to be launched from rest from the earth’'s surface and is to reach a maximum height of 990 m above the earth'’s surface. The rocket’'s engines give the...

Homework Statement Analyze the specific heat of a one dimensional lattice of identical atoms: Show within Debye approximation that the specific heat at low temperatures ( ≪ Θ) is proportional to T/ΘD . Here ΘD=ℏD/ kB = ℏvs/KBa is the Debye temperature valid for 1D, kB the Boltzmann...

Hello, I am working in 1D here. For the ferromagnetic Ising model ##H = -\sum_k X_k X_{k+1}## (or ##H = -YY##) we know that the ground state is gapped and has a twofold degeneracy due to SSB (spontaneous symmetry breaking) of the spin flip symmetry ##P = Z_1 Z_2 Z_3 \cdots##. I am now...

Homework Statement The system is a chain of atoms in 1D length L and number of atoms N. and \epsilon_k=\hbar c_s k a) What is the density of states? b)The number of states that can be occupied (use boundary conditions) c) Determine w_d(I think this is the debye frequency) in terms of N,L,k...

Homework Statement Show that for the one-dimensional linear harmonic oscillator the Hamiltonian is: [; H = \frac{1}{2}[P^2+\omega ^2 X^2]-\frac{1}{2}\omega \hbar ;] [; =\frac{1}{2}[P+i\omega X][P-i\omega X]+\frac{1}{2} \omega \hbar ;] where P, X are the momentum and position operators...

Homework Statement An electron in a one-dimensional box with walls at x =(o,a) is in the quantum state psi = A o<x<a/2 psi = -A a/2<x<a A) obtain an expression for the normalization constant, A. B) What is the lowest energy of the electron that will be measured in this state...

Homework Statement A flowerpot falls off a windowsill and falls past the window below. You may ignore air resistance. It takes the pot 0.420 s to pass from the top to the bottom of this window, which is 1.90 m high. Part A How far is the top of the window below the windowsill from which the...

Homework Statement a particle of mass m moves in 1D potential V(x),which vanishes at infinity. Ground state eigenfunction is ψ(x) = A sech(λx), A and λ are constants. find the ground state energy eigenvalue of this system. ans: -ħ^2*λ^2/2m Homework Equations <H> =E, H = Hamiltonian. p=...

Homework Statement [/B] Don't know if this goes here or in the advanced bit, thought I'd try here first! I know the general solution of a 1D wave equation is given by d'Alembert's formula ##u(x,t) = 0.5[u(x+vt,0) + u(x-vt,0)] + \frac{1}{2v} \int_{x-vt}^{x+vt} \frac{\partial u}{\partial...

The ground state wave-function of a 1-D harmonic oscillator is $$ \psi(x) = \sqrt\frac{a}{\sqrt\pi} * exp(-\frac{a^2*x^2}{2}\frac{i\omega t}{2}). $$ a) find Average potential energy ? $$ \overline{V} = \frac{1}{2} \mu\omega^2\overline{x^2} $$ b) find Average kinetic energy ? $$ \overline{T} =...

Consider the Lindhard response function: \chi(\vec{q})=\int\frac{d\vec{k}}{(2\pi)^d}\frac{f_\vec{k}-f_{\vec{k}+\vec{q}}}{\epsilon_\vec{k}-\epsilon_{\vec{k}+\vec{q}}} where ##\vec{q}## is the wavevector, ##\epsilon## is the free electron energy and ##f## is Fermi-Dirac distribution function. For...

Hi, Consider model of one dimensional spin chain with a random couplings J. The Hamiltonian is the following: $$ H = \sum_i J_i (S_i^x S_{i+1}^x+ S_i^y S_{i+1}^y)$$, Which by Jordan-Wigner transformation we can transform it to the fermionic representations. $$ H = \sum_i J_j/2 (c_i...

Hey, I'm stuck halfway through the solution it seems. I could use some tips on how to continue. 1. Homework Statement I have to determine a linear combination of the states |0\rangle, |1\rangle, of a one dimensional harmonic oscillator, so that the expectation value \langle x \rangle is a...

I am trying to set up the mass matrix for a 1D system which I want to solve using finite elements. So the mass matrix is defined as M = \int{NN^T}dL, where N is the finite element linear basis functions. I use hat functions. Say I have 10 elements, corresponding to 11 nodes running from -5...

Hey there. While studying the Single-particle Level Density, I encountered the example in the image below, referring to the One-dimensional Box problem. However, I do not understand what is it that he call's F(E), neither how does one go from that, to the density of states in Equation (3.64)...

Homework Statement The polyacetylene chain is a 1D chain of Carbon atoms with single bonds and double bonds in succession. Spacing for single bond is ##a_s = 0.144~nm## and spacing for double bond is ##a_d = 0.136~nm##. Describe the structure using a "lattice" and a "basis". Sketch the...

Suppose the pdf is A*exp(-mv^2/2kT) , where A is the normalization constant. To obtain A I would integrate the pdf over the all possible values of v. The question is, should the limits be (-infinity,infinity) or [0,infinity) ? It seems that only by choosing the former can I get the correct...

Homework Statement Calculate the focal length of 1D Fresnel lens, whose transmittance is given as $$T(\xi)=\frac 1 2(1+\cos(\alpha \xi ^2)).$$ Homework Equations Anything you wish The Attempt at a Solution I have no idea. I tried to use the equation for diffraction image $$u_p=C\int _0...

Homework Statement Compute correlation functions ##<\sigma_r \sigma_{r+l}>## for the 1D Ising model of length L with the follow BD conditions (i) Periodic (ii) Anti-Periodic (iii) ##\sigma_1 = \sigma_{L+1}=1## (iv) ##\sigma_1= -\sigma_{L+1}=1## Homework Equations ##<\sigma_r \sigma_{r+l}> =...

Homework Statement Hello, I'm just curious as to whether I'm going about solving the following problem correctly... Problem Statement: A particle mass m and charge q is in the ground state of a one -dimensional harmonic oscillator, the oscillator frequency is ω_o. An electric field ε_o is...

Hi all, I have almost finished my dissertation on using the finite element method to solve the 1D version of the Poisson equation. For the last section I would like to run through a couple of examples but am struggling to find some. Obviously I can make up any equations that satisfy the...

Homework Statement [/B] 1)Which describes the 1D gravitational force in this figure. (+x is to the right.) a)Something else. b)Fgrav=−GMmx2 c)Fgrav=+GMmx22)In moving the little mass m from x1 to infinity the force of gravity does _____________ work. a) positive b) negative c) no I added an...

Hi, I'm doing a 1D thermal conduction simulation on Comsol Multiphysics 4.4 and my first component is vacuum. I did'nt found the vacuum in the material list. Should I create a new component with a null thermal conductivity ? Thanks

Homework Statement We're given an unnormalized state function ψ(x) of an electron in a 1 dimensional box of length pi. The state function is a polynomial. We're asked to find the probability that a measurement of its energy would find it in the lowest possible energy state. Homework Equations...

Homework Statement If a one-dimensional box is 1 nm long, what is the probability of finding the particle between the following limits? (a) x = 0 nm and x = 0.05 nm (b) x = 0.55 nm and x = 0.65 nm Homework Equations ψ = (2/L)½ sin(πx/L) The Attempt at a Solution (I do chemistry and I'm really...

Hi, I've been doing some work on the finite element method. I have been able to calculate the stiffness matrix and load vector and apply both homogeneous and inhomogeneous Dirichlet conditions but am stuck on calculating the Neumann conditions. I have the definition of it as...

Homework Statement Two frictionless pucks are placed on a level surface with an initial distance of 20.0 m. Puck 1 has a mass of 0.80 kg and a charge of + 3 E-4 C while puck 2 has a mass of 0.4 kg and a charge of +3 E-4 C. The initial velocity of puck 1 is 12 m/s [E] and the initial velocity...

Homework Statement - A Dragster at the starting line accelerates at 8 m/s^2 to the finish line. If it took 4.6 s, how long is the track? - The Dragster deccelerated to a stop in 100m. How long did it take?Homework Equations x = 0 + 1/2at^2 The Attempt at a Solution The first part of the...

Hello, this is my first post on PhysicsForums. I'm a first year student at the University of Kansas pursuing a Bachelor of Science in Physics and Astronomy (double majoring). The wording on my homework (for Honors General Physics 1) is a little bit strange to me so maybe some of you guys and...

Homework Statement You have a potential well, it's 1-dimensional and has a width of 0 to a. All of a sudden the wall of the well is pushed inward so that it's half as wide. Now the well is only extending from 0 to a/2. in the well is a particle (mass m) that is in the first excited state...

The electronic structure of CNT is discussed on the basis of band structure of graphene. Graphene has a linear dispersion relation: E = h_cut vF |k| where k is the 2D wavevector and vF is the Fermi velocity. CNTs are macroscopic along the axis but have a circumference of atomic dimensions, which...

Homework Statement Find the ground and first excited state eigenfunctions of for the 1D infinite square well with boundaries -L/2 and +L/2 Homework Equations $$\frac{-\hbar^2}{2m}\frac{\partial^2}{\partial x^2}\psi(x) = E\psi(x)$$ The Attempt at a Solution Okay so I know how to solve it and...

Hi, I'm working on a problem that requires me to calculate thermal energy (kT) at different temperatures and compare those values to the lowest state energy of a particle in box (1D) of varying lengths. I've calculated the ground-state energies of the electron in all of these different sized...

Homework Statement A simple model of a polymer undergoing a helix-coil transition is to describe the polymer in terms of N equal length segments, each of which can be in either a coil or a helix state. A more realistic model also takes into account the energy cost associated with a boundary...

Hello, I have a three dimensional FDTD code. The problem I have for simulation is one dimensional. How can I use this 3D FDTD code for the 1D problem. The 1D problem is like this: in one-dimension half of the problem space is filled with a dielectric medium and the other half is free-space. A...

Image is a set of 1D potentials which i need more examples and their solutions containing transmitting states, bounded states, scattering states and coefficients. I searched with "1D potential combinations" "1D potential set" keywords but can not find anything yet. Which keyword should i...

Hi there, I am trying to understand the dispersion curve(as shown below) of a 1D lattice with diatomic basic. Here are my questions 1) Can both optical and acoustic branch of phonon can simultaneously exist in crystal? 2)Why there is a band gap between optical and acoustic phonon...

Homework Statement For a nitrogen molecule, calculate the lowest 2 energy levels and the characteristic temperature; Mass of molecule = 2.33x10-26[kg] Length of box = 10-9[m]Homework Equations E = n2.h2/8mL2 (n=1,2,3,...) Characteristic Temperature (Tc) -> when thermal energy kBT =...

Homework Statement Show that for a 1d potential V (-x)=-V (x), the eigen functions of the Schrödinger equation are either symmetric/ anti-symmetric functions of x.Homework EquationsThe Attempt at a Solution I really don't know how to do it for odd potential. Let me show you how I am doing it...

Homework Statement Obtain the critical exponents for specific heat, susceptibility, and the order parameter (magnetization). Homework Equations $$A = -k_B T N \ln \left[e^{\beta J} \cosh (\beta h) +\sqrt{ e^{2\beta J}\sinh^2 \beta h + e^{-2\beta J} }\right]$$ $$\left<m \right> \propto...

Homework Statement http://puu.sh/bTtVx/ba89b717b8.png Homework Equations I've tried using the integral method of Schrodinger's eq, getting: (X/L - (1/4pi)sin(4xpi/L) from x1 to x2. The Attempt at a Solution I've tried plugging in the values of x given in the problem to the above equation...

Homework Statement The height of a helicopter above the ground is given by h = 3.30t3, where h is in meters and t is in seconds. After 1.80 s, the helicopter releases a small mailbag. Assume the upward direction is positive and the downward direction is negative. Already solved for Initial...

Homework Statement Prove that in the 1D case all states corresponding to the discrete spectrum are non-degenerate. Homework Equations \hat{H}\psi_n=E_n\psi_n The Attempt at a Solution Okay so, what I am stuck on here is that the question is quite broad. I can think of specific...

Homework Statement This is a Quantum Physics problem. An electron moves in a one-dimensional potential well such that the potential V = 0 for |x| ≤ a, and V = ∞ otherwise. The system has energy eigenfunctions: Un = a^(-1/2) cos (n∏x/2a), for n odd, and Un = a^(-1/2) sin (n∏x/2a)...

Hi all, I'm doing a project on the finite elements method and am struggling to understand a part of it. I have defined the hat functions as: \[ \phi_i(x) = \begin{cases} \frac{x-x_{i-1}}{h} & \text{if } x_{i-1}\leq x<x_i \\ \frac{x_{i+1}-x}{h} & \text{if } x_i\leq x<x_{i+1}\\ 0 &...

Homework Statement Trying to construct Shrodinger Equation given: * mass: m * Boundary Conditions: (potential) V(x)=-Vo exp(-x/L) for 0<x≤L V(x)=∞ for x≤0 Homework Equations The Attempt at a Solution (-h^2 / 2m ) (d^2 ψ / dx^2) + V(x)ψ = E * psi Not sure how to incorporate...

So my professor said that the Kinetic energy of the particle in a 3D infinite well is dependent on position where in a 1D infinite well it's NOT dependent on position. She is sort of notorious for being wrong apparently and many of my undergrads are telling me she is wrong. I understand that...

So starting from the time dependent schrodinger equation I perform separation of variables and obtain a time and spatial part. The spatial part is in effect the time independent schrodinger equation. Since we are dealing with a free particle I can take the time independent equation, set V = 0...