Harmonic oscillator Definition and 699 Threads

The frequency of a harmonic oscillator is (as you know) f=\frac{1}{2\pi}\sqrt{\frac{k}{m}} I am wondering if this equation only applies for massless harmonic oscillators (or oscillators oscillating sideways)? The proof for the equation above is \sum {F=ma} -kx=ma...

The question is as follows: Suppose that, in a particular oscillator, the angular frequency w is so large that its kinetic energy is comparable to mc2. Obtain the relativistic expression for the energy, En of the state of quantum number n. I don't know how to begin solving this question. I...

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...

Hi, Why is it that the WKB approximation produces the correct eigenvalues for the Harmonic Oscillator problem, but the wrong wavefunctions, whereas for the square well, we get correct wavefunctions and the wrong eigenvalues? I've been trying to dig through the approximations we make in...

The one dimensional harmonic oscillator is associated with the group U(1) and the three dimensional harmonic oscillator is associated with the group SU(3). Is their a group associated with the two dimensional harmonic oscillator? Thank you for any thoughts.

The 3-dimensional harmonic oscillator has SU(3) symmetry. This is stated in many papers. It seems to be due to the spherical symmetry of the system. (After all, the idea of a 3d harmonic oscillator is that a mass is attached to the origin with a spring, and that the mass can move in 3...

Homework Statement The wave function \Psi(x,t) ofr the lowest energy state of simple harmonic oscillator, consisting of a particle mass m acted on by a linear restoring force F=Cx, where C is the force constant, can be expressed as.. \Psi(x,t)=Aexp[-(\sqrt{}Cm/2h)x^{}2-(i/2)(\sqrt{}C/m)t]...

Homework Statement Suppose there is a square plate, of side a and mass M, whose corners are supported by massless springs, with spring constants K, K, K, and k <= K (the faulty one). The springs are confined so that they stretch and compress vertically, with unperturbed length L. The...

Homework Statement Hi all. At time t<0 a particle is in the stationary state \left| {\psi _0 } \right\rangle of the harmonic oscillator with frequency omega1 (i.e. the ground state of the H.O.). At t=0 the Hamiltonian changes in such a way that the new angular frequency is omega =...

Homework Statement A damped harmonic oscillator is driven by a force F external= F sin (omega * t) where F is a constant, and t is time. Show that the steady state solution is given by x(t)= A sin (omega * t - phi) where A is really A of (omega), the expression for the amplitude...

How to find the probability density function of a simple harmonic oscillator? I know that for one normal node is should be a parabola but what is the formula and how do we derive it?

Thanks for all the help on the first question but now I have to solve for <T>. I have no idea how to do this, and I could use some help for a kick start. thanks!

first post! but for bad reasons lol Im trying to find <x> and <p> for the nth stationary state of the harmonic potential: V(x)=(1/2)mw^2x^2 i solved for x: x=sqrt(h/2mw)((a+)+(a-)) so <x> integral of si x ((a+)+(a-)) x si. therefor the integral of si(n+1) x si + si(n-1) x si. si(n+1)...

In quantum mechanics, one of the major concerns is the propagator determination of the system. The propagator is completely expressed in terms of its classical in the Van-Vleck Pauli Formula. In a harmonic oscillator in a time dependent force, the Lagrangian is given by...

damped harmonic oscillator, urgent help needed! Homework Statement for distinct roots (k1, k2) of the equation k^2 + 2Bk + w^2 show that x(t) = Ae^(k1t) + Be^(k2t) is a solution of the following differential equation: (d^2)x/dt^2 + 2B(dx/dt) + (w^2)x = 0 Homework Equations The...

If a mass that hangs suspended vertically from a spring is increased, then won't the period increase as a direct linear proportion? (Because the larger mass has a greater inertia and will require a larger force and longer time to change the direction of motion on each oscillation?) Some...

1. Homework Statement and the attempt at a solution Please see attached. I'm not so sure if my problem lies with the physics or the mathematics. I have the distinct feeling that it's the latter and that I'm missing something elementary, but truly have no idea how to proceed. Any...

Hello, how do I compute the transition amplitude of the forced harmonic oscillator with the method of path integration? Regards, Mr. Fogg

Homework Statement Show that, [a, \hat H] = \hbar\omega, [a^+, \hat H] = -\hbar\omega Homework EquationsFor the SHO Hamiltonian \hat H = \hbar\omega(a^+a - \frac{\ 1 }{2}) with [a^+, a] = 1 [a, b] = -[b, a] The Attempt at a Solution I have tried the following: [a, \hat H] = a\hat...

Homework Statement This is supposed to be a question for high school seniors who've had instruction in introductory concepts of special relativity and non-relativistic QM. According to my TA, he isn't too certain if it can be done within these confines but nonetheless I've attempted the...

I have the following equation subject to y(0)=0 and y'(0) = 0 my'' + b y' + k y = C I have done an experiment where I measured force at given depth for a dampened harmonic oscillator. Is it possible to use the force I measured to solve for displacement and then back out coefficient b for...

A 50.0-g mass connected to a spring with a force constant of 35.0 N/m oscillates on a horizontal, frictionless surface with an amplitude of 4.00 cm. Find the speed of the mass when the displacement is 1.00 cm. Can I use here something like : \frac{mv2}{2}=0,5kx2?

Many quantum physics/chemistry books use Schrodinger's equation to derive a differential equation which describes the possible wavefunctions of the system. One form of it is this: \frac{d^{2}\psi}{dx^{2}} + (\lambda - a^{2}x^{2})\psi = 0 "a" and lambda are constants. Most books solve this...

How to describe a harmonic oscillator defined by H(q,p) = \frac{p^2}{2m} + \frac{1}{2}kq^2 in a heat bath with some fixed temperature T? I suppose this question alone is not quite well defined, because it mixes classical and statistical mechanics in confusing manner, but I thought that one...

I have trouble understanding how damping affects the period (of a torsion pendulum). I know that damping affects the amplitude of the oscillator, however how would damping change the period then? I have a feeling this has to do with angular frequency, w, given by: w = sqrt( (k/m) -...

Homework Statement Given a particle is confined in a one dimensional harmonic oscillator potential, find the matrix representation of the momentum operator in the basis of the eigenvectors of the Hamiltonian. Homework Equations Potential: V(x) = 0.5 m w^2 x^2 where m is the mass of...

I am looking into the calculations of a harmonic oscillator potential for nuclei single-particles. The information I am looking at is at: http://en.wikipedia.org/wiki/Shell_model the specific section “Deformed harmonic oscillator approximated model” The specific question is, I don’t...

Homework Statement A particle moves along x-axis subject to a force toward the origin proportional to -kx. Find kinetic (K) and potential (P) energy as functions of time t, and show that total energy is contant. Homework Equations K = (1/2)m*v^2 P = (1/2)k*x^2 E = K+P x = Asin(wt...

Does anyone know why a harmonic potential gives rise to coherent states? In other words, what is special about a quadratic potential that causes the shifted ground state to oscillate like a classical particle without dispersing so as to saturate the uncertainty principle? Any help or insight...

Homework Statement A simple harmonic oscillator consists of a block of mass 2.30 kg attached to a spring of spring constant 440 N/m. When t = 1.70 s, the position and velocity of the block are x = 0.135 m and v = 3.130 m/s. (a) What is the amplitude of the oscillations? What were the (b)...

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 A damped harmonic oscillator originally at rest and in its equilibrium position is subject to a periodic driving force over one period by F(t)=-\tau^2+4t^2 for -\tau/2<t<\tau/2 where \tau =n\pi/\omega a.) Obtain the Fourier expansion of the function in the integral...

Hi, does anyone know of a good resource that focuses on the history of the harmonic oscillator and other classical systems like the vibrating string and vibrating drum? I need to talk about the historical aspect in a project and was having a hard time finding some good material. anyway let me...

Homework Statement An un-damped driven harmonic oscillator satisfies the equation of motion: ma+kx=F(t) where we may write the un-damped angular frequency w-naught^2=k/m. The driving force F(t)=F-naught*sin(wt) is switched on at t=0. Find x(t) for t>0 for initial conditions x=0, v=0,at t=0...

Homework Statement A car is moving along a hill at constant speed on an undulating road with profile h(x) where h'(x) is small. The car is represented by a chassis which keeps contact with the road , connected to an upper mass m by a spring and a damper. At time t, the upper mas has...

See post two.

Homework Statement A driven oscillator satisfies the equation x'' + omega2=F0cos(omega(1+episilon)t] where episilon is a positive constant. Show that the solution that satisfies the iniitial conditions x=0 and x'=0 when t=0 is x= (F0*sin(.5episilon*omega * t)...

I have been given at t=1.00 a position and velocity. And the spring constant and mass. I have found the maximum amplitude. The question is, where was the block at time t=0? And apparently this can be done without solving for the phase constant and making an equation. The question doesn't...

Hi all, I have to determine the potential energy of a hanging spring with a mass m in the end and spring constant k. I try to write down the force in the system F = m*g + k*x and integrate the force in order to get the potential energy E_p = m*g*x+0.5*k*x*x Does this look correct...

Homework Statement Predict the wavenumber (cm-1) position of infrared absorption due to fundamental vibration from v=0 to v=1 and 2nd overtone from v=0 to v=3. For a harmonic occilator whose frequency=8.00x1013 s. Homework Equations Energy expression for harmonic oscilator: Ev=...

I am working with the following harmonic oscillator formula. \psi_n \left( y \right) = \left( \frac {\alpha}{{\pi}} \right) ^ \frac{1}{{4}} \frac{1}{{\sqrt{2^nn!}}}H_n\left(y\right)e^{\frac{-y^2}{{2}}} Where y = \sqrt{\alpha} x And \alpha = \frac{m\omega}{{\hbar}} I...

We have a potential that is (1/2)kx^2 for x>0 and is infinity for x<0 ( half harmonic oscillator. Now i want to calculate the bound states of the system for given E. My question is this: Do we apply 1. \int p(x) dx = (n - \frac{1}{4} ) h ( Since there is only one turning point that can...

The displacement of a harmonic oscillator is given by x = A Cos(wt + Phi) The phase angle phi is equally likely to have any value in the range 0 < Phi < 2Pi, so the probability W(Phi) that Phi lies between Phi and Phi + delta-Phi is delta-Phi/(2Pi). For a fixed time t, find the probability...

Homework Statement Hello. I am attempting to evaluate the classical action of a harmonic oscillator by using the Euler-Lagrange equations. Homework Equations The Lagrangian for such an oscillator is $$ L=(1/2)m(\dot{x}^2-\omega^2 x^2) $$ This is easy enough to solve for. The classical action...

I wish to graph a couple of the waveforms of a harmonic oscillator. I have consulted several resources and have found two that I like but the final equation differs even though they are both labeled normalized harmonic oscillator wavefunction. The first reference explains how the harmonic...

1. At a certain time the wavefunction of a one-dimensional harmonic oscillator is \psi(x) = 3\phi0(x) + 4\phi1(x) where \phi0(x) and \phi1(x) are normalized energy eigenfunctions of the ground and first excited states respectively. Normalize the wavefunction and determine the probability...

Alright, I'm sure I'm missing something extremely simple, but in Griffiths (and another text I'm reading) coherent states are mentioned as eigenfunctions of the annihilation operator. I just don't understand: a) how you can have an eigenfunction of the annihilation operator (other than |0>) if...

I'm reading Griffiths', and I had a question about the harmonic oscillator. Griffiths solves the Schrodinger equation using ladder operators, and he then says that there must be a "lowest rung," or \psi_{0}, such that a_\psi_{0} = 0. I'm guessing this also means that E = 0 for a_\psi_{0}...

Homework Statement A particle oscillates between the points x = 40mm and x = 160mm with an acceleration a = k(100-x) where k is a constant. The velocity of the particle is 18mm/s when x=100 and zero at x = 40mm and x = 160mm. Determine a) the value of hte constant k, b) the velocity when x =...

Problem Show that in the nth state of the harmonic oscillator \langle x^2 \rangle = (\Delta x)^2 \langle p^2 \rangle = (\Delta p)^2 Solution This seems too simple... I'm not sure if it's correct... It is obvious that \langle x \rangle = 0... this is true because the parity of the...