Harmonic oscillator Definition and 743 Threads

Hi I'm having problems with solving this question: a 90.0 kg skydiver hanging from a parachute bounces up and down with a period of 1.50 seconds. What is the new period of oscillation when a second skydiver, whose mass is 60.0 kg, hangs from the legs first? the answer is 1.94 seconds...

I'm sorry if the form of my post does not meet the general requirements(this is the first time i work with any kind of LaTeX) and I promise that my next posts will be more adequate. Right now I am in serious need of someone explaining me this problem, since on the 6th of June I'm supposed to...

I'm solving the 2D harmonic oscillator, numerically. -\frac{1}{2}\left( u_{xx} + u_{yy}\right) + \frac{1}{2}(x^2+y^2)u = Eu The solutions my solver spits out for say, the |01> state, are linear combinations of the form |u\rangle = \alpha_1 |01\rangle + \alpha_2 |10\rangle which is...

Homework Statement Folks, I am looking at a past exam question regarding the Harmonic Oscillator. The question ask 'Justify that the ground state of a harmonic oscillator a_\psi_0=0 equation 2.58 on page 45 of griffiths. THis was not covered in my notes. Any ideas how to justify this...

Homework Statement Greetings, gents. I have a modelization problem you might be able to help me with... I have two oscillators, modeled as: osc_{1}=\cos{(a z)}osc_{2}=\cos{(\frac{b}{z})} and a resonance condition f(z) when these two oscillators are combined, modeled as...

Why the reciprocal of the damping rate in this model equal to the phonon lifetime? Can somebody give me a detailed exaplanation. Thanks.

Hi there, I just started an intermediate classical mechanics course at university and was smacked upside the head with this question that I don't know how to even start. Homework Statement We are to find the response function of a damped harmonic oscillator given a Forcing function. The...

Homework Statement The period of a macroscopic pendulum made with a mass of 10 g suspended from a massless cord 50 cm long is 1.42 s. (a) Compute the ground state (zero-point) energy. (b) If the pendulum is set into motion so that the mass raises 0.1 mm above its equilibrium position, what will...

Homework Statement http://img191.imageshack.us/i/questionyw.png/ Homework Equations Given in problem The Attempt at a Solution a) I've been able to find expressions of operators x, p_x, y and p_y in terms of the creation/annihilation operators and hence been able to express the...

i have a quick question A particle in ground state of a S.H.O whose potential is given by V_1(X)=\frac{1}{2}mw^2_1x^2 suddenly changes to V_2(X)=\frac{1}{2}mw^2_2(x-x_o)^2 what is the wavefunction going to be like for the new potential? i'd think everything else stays the same in the...

Hello, I want to find <xftf|x(t)|xiti> in harmonic oscillator. I tried to insert the complete set of energy eigenstates to the right and the left side of x(t), but it yields somewhat more complicated stuff. Thank you

Homework Statement a block of mass m=.5kg is sliding on a horizontal table with coefficients of static and kinetic friction of .8 and .5 respectively. It is attached to a wall with a spring of unstretched length l=.13m and force constant 200 n/m. The block is released from rest at t=0 when...

Homework Statement There is a block attached to the wall via a spring. The only damping force is friction, where there is kinetic and static. Homework Equations m(d^2x/dt^2)=-kx-? The Attempt at a Solution I can solve this, except usually the damping force is given as...

Homework Statement a particle of mass m moving in one dimension has potential energy V(x)=0.5m [[omega(subscript0)]^2] x^2 verify that psi0 (proportional to) exp [(-m omega0 x^2)/2 h bar] and psi1 (proportional to) exp [(-m omega0 x^2)/2 h bar] are both solutions of the time...

Homework Statement I'm talking about the probability density plot of the harmonic oscillator. Is there some physical meaning to be extracted from this? Here's a link that contains the drawing of what I'm talking about http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc5.html...

Homework Statement The question states for a harmonic oscillator the wavefunction is: \mu = C*x*exp(-\alphax2/2) it then wants you to find \alpha. using the standard hamiltonian: H = -\hbar/2m d2/dx2 + 1/2 mw2x2 I have differentiated \mu twice and put it into the TISE. for the left hand...

Homework Statement A particle is in the ground state of a harmonic oscillator with classical frequency w. Suddenly the classical frequency doubles, w -> w' = 2w without initially changing the wavefunction. Instantaneously afterwards, what is the probability that a measurement of energy...

Homework Statement We know that a particle in SHM is in a state such that measurements of the energy will yield either E_0 or E_1 (and nothing else), each with equal probability. Show that the state must be of the form \psi = \frac{1}{\sqrt2} \psi_0 + \frac{e^{i \phi}}{\sqrt2} \psi_1 where...

Homework Statement Hi guys. I've been working on this problem for a while, it's starting to frustrate me. "Show that the function of Ѱ=e^(-bx^2) with b=mw/2ħ is a solution and that the corresponding energy is ħw/2." Homework Equations Schrodinger Eqn...

Homework Statement In the time interval (t + δt, t) the Hamiltonian H of some system varies in such a way that |H|ψi>| remains finite. Show that under these circumstances |ψi> is a continuous function of time. A harmonic oscillator with frequency ω is in its ground state when the stiffness of...

In the attached file, I have formulated a simple one dimensional harmonic oscillator and solved the model numerically. Such a model might represent a simple reaction coordinate along which a liquid drop actinide nucleus might split after absorbing a neutron. Clearly the complete model involves...

Pleae help me. a),b),c) was already solved. but question d) is not.

uncertainty relation. I think I'm on the right track. Currently, I'm at, E = (1/2m)*<p^2> + (1/2)*k*<x^2> and when applying the uncertainty relation, deltax = <x^2>^(1/2) deltap = <p^2>^(1/2) How do I go about connecting everything from here? Thanks!

Homework Statement A particle of mass m that is confined to a harmonic oscillator potential V(x) = \frac{1}{2} m \omega^2 x^2 is described by a wave packet having the probability density, |\Psi (x,t) |^2 = \left(\frac{m\omega}{\pi\hbar} \right )^{1/2}\textrm{exp}\left[-\frac{mw}{\hbar}(x -...

Homework Statement Verify that the ground state (n=0) wavefunction is an eigenstate of the harmonic oscillator Hamiltonian. Using the explicit wavefunction of the ground state to calculate the average potential energy <0|\hat{v}|0> and average kinetic energy <0|\hat{T}| 0> Homework...

Homework Statement A simple harmonic oscillator of force constant 2*106 N/m and amplitude .01 m has total maechanical energy 160 J... Homework Equations The Attempt at a Solution Now this is not the question but what is the minimum potential energy...1/2kx^2 comes out to be...

1. Homework Statement Show that bohr's hypothesis (that a particle's angular momentum must be an integer multiple of h/2pi) when applied to the three dimensional harmonic oscillator, predicts energy levels E=lh/pi w with l = 1,2,3. Is there an experiment that would falsify this prediction...

The TISE can be written as -\frac{\hbar^{2}}{2m}\frac{d^{2}u}{dx^{2}} + \frac{1}{2}m\omega_{0}^{2}x^{2}u = Eu Now my lecture notes say that it is convenient to define scaled variables y = \sqrt{\frac{m\omega_{0}}{\hbar} x} and \alpha = \frac{2E}{\hbar\omega_{0}} Hence \frac{d}{dx} =...

It is well known that for an isolated system, the normal mode frequency of a N-body harmonic oscillator satisfies Det(T-\omega^{2}V)=0. How about a non-isolated, fixed temperature system? In solid state physics I have learned that in crystal the frequency does not change, but the amplitude of...

Homework Statement A particle in the ground state of the harmonic oscillator with classical frequency \omega, when the spring const quadruples (so \omega^{'}=2\omega) without initially changing the wave function. What is the probability that a measurement of the energy would still return the...

I have a planar molecule with a torsional oscillation mode where it twists around a C-C bond by an angle \theta from some equilibrium position. The restoring force is a function of theta, and the potential energy involved is given by V(\theta) = V_0(1-cos(2\theta)) I need to "use a Taylor...

Homework Statement The particle with the mass m is in 2D potential: V(r)=\frac{m}{2}(\omega_x^2x^2+\omega_y^2y^2),\quad \omega_x=2\omega_y, and is described with wave package for which the following is valid: \langle x\rangle (0)=x_0,\ \langle y\rangle (0)=0,\ \langle p_x\rangle (0)=0\...

Homework Statement The pendulum of a grandfather clock has a period of 1s and makes excursions of 3cm either side of dead centre. Given that the bob weighs 0.2kg, around what value of n would you expect its non negligible quantum amplitudes to cluster? Homework Equations [/B] The...

Hi! Info: This is a rather elementary question about the creation a(+) and annihilation (a-) operators for the 1D H.O. The problem is to calculate the energy shift for a given state if the weak perturbation is proportional to x⁴. Using first order perturbation theory for the...

So here is the problem. A mass hanging from a spring is modeled by the operator L(y)=2y"+y'/10+2y (y=0 corresponds to hanging equilibrium). Assume mass starts with y(0)=1 and y'(0)=1. Assume an upward impulsive force of mag M is applied at the first possible time which results in complete end...

Hello, Attached are two problems I can not solve, thanks for the help. The Attempt at a Solution For the first question, I understand that I need insert A1coswt+A2sinwt into the homogenous equation , but don't know what's then .. But I'm pretty much lost on both of em :(

Homework Statement Ok so the question is, is the state u(x) = Bxe^[(x^2)/2] an energy eigenstate of the system with V(x) = 1/2*K*X^2 and what is the probability per unit length of this state.Homework Equations The Attempt at a Solution So the way i did this was, to find if the state is an...

A particle of mass m moves along the x-direction such that V(x)=½Kx^2. Is the state u(¥)=B¥exp(+¥2/2), where ¥ is Hx (H = constant), an energy eigenstate of the system?. What is probability per unit length for measuring the particle at position x=0 at t=t0>0?

Homework Statement Given that a^+|n\rangle=\sqrt{n+1}|n+1\rangle a|n\rangle=\sqrt{n}|n-1\rangle and that the other eigenstates |n> are given by |n\rangle=\frac{(a^+)^n}{\sqrt{n!}}|0\rangle where |0> is the lowest eigenstate. Define for each complex number z the coherent state...

Imagine a fictitious universe where springs want to stretch: the spring force is proportional to, and in the same direction as, displacement from equilibrium. We'll call these anti-springs. (a) Set up a differential equation modeling the motion of a damped anti-spring if the mass is m = 1 kg...

Homework Statement Given the Hamiltonian for the harmonic oscillator H=\frac{p^2}{2m}+\frac{1}{2}m\omega^2 x^2 , and [x,p]=i\hbar . Define the operators a=\frac{ip+m\omega x}{\sqrt{2m\hbar \omega}} and a^+=\frac{-ip+m\omega x}{\sqrt{2m\hbar \omega}} (1) show that [a,a^+]=1 and that...

My answer would be "yes," and here's my argument: If we let H = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} + \frac 12 m \omega^2 x^2, it is a Hermitian operator with familiar normalized eigenfunctions \phi_n(x) (these are products of Hermite polynomials and gaussians) and associated...

Hi, I don't understand why the momentum probability distribution of the quantum mechanical oscillator has the same shape as the position probability distribution (with peaks at the extremes), I mean, I understand the mathematics but I don't understand the concept. This is my reasoning (which...

Homework Statement Show that G(q_2,q_1;t)=\mathcal{N}\frac{e^{iS_{lc}}}{\sqrt{\det A}} where \mathcal{N} is a normalization factor independent of q1, q2, t, and w. Using the known case of w=0, write a formula for G such that there is no unknown normalization factor. Homework Equations I...

Homework Statement What is the probability that a particle in the ground state of a simple harmonic oscillator 1-D potential will be found outside the region accessible classically Homework Equations ∫(between 1 and infinity) e^(-y^2 ) dy=0.08π^(1/2) I feel like it's quite a...

Homework Statement Show that U*(pi/(2*omega)) |x> is an eigenvecor of p and specify its eigenvalue. Similarly, establish that U*(pi/(2*omega)) |p> is an eigenvector of x. Homework Equations U*(t) = exp((i/h_bar)H*t) The Attempt at a Solution I've tried using closure with P...

Homework Statement A particle is moving in a simple harmonic oscillator potential V(x)=1/2*K*x^2 for x\geq0, but with an infinite potential barrier at x=0 (the paddle ball potential). Calculate the allowed wave functions and corresponding energies.Homework Equations I am thinking that the...

Homework Statement Harmonic oscillator is in the first excited state |1> when a constant electric field E is switched on. Find the time evolution of the wave functionHomework Equations Schrodinger equation H\Psi = E_n\Psi H = \frac{P^2}{2m} + \frac{m\omega^2x^2}{2}-qEx The Attempt at a...

For part of my lab write up on pendulum motion, my professor wanted us to find out why a pendulum was not a simple harmonic oscillator, and under what conditions it was. He also wanted to show this mathematically. So far what I have is that if there is no damping(friction?) and if the the...

I am supposed to find the number of mircostates for the following Hamiltonian \ \begin{equation} \Sigma {(q_n+mwp_n)^2}<2mE \end{equation} So I am attempting to take the integral as follows \ \int e^{(q_n+mwp_n)^2} d^{3n}q d^{3n} p [tex\] I found a solution that tells me \...