Oscillator Definition and 1000 Threads

Homework Statement For a quantum oscillator find all non-zero matrix elements of the operators ##\hat{x}^3## and ##\hat{x}^4## Homework Equations ##\hat{x} = \sqrt{\frac{\hbar}{2m\omega}}\left(a+a^\dagger\right)## ##a^\dagger |n\rangle = \sqrt{n+1}|n+1\rangle## ##a |n\rangle =...

I have the following homework problem that I am having trouble with. Any guidance would be appreciated. Thank you in advance. Consider an object hanging on a spring, immersed in a cup of water. The water exerts a linear viscous force -bv on the object, where v is the speed of the object...

Hi people! Today I was doing some QFT homework and in one of them they ask me to calculate the Harmonic Oscillator propagator, which, as you may know is: W(q_2,t_2 ; q_1,t_1) = \sqrt{\frac{m\omega}{2\pi i \hbar \sin \omega (t_2-t_1)}} \times \exp \left(\frac{im\omega}{2\hbar \sin \omega...

Hey guys, I'm new here so id just like to say hello my name is John. Anyway, I'm writing a lab report on a torsional oscillator with magnetic dampers, and I'd like to know some historical background on natural frequencies and damping. Does anyone know who the first physicist to study...

how to compute <n|ξ^4|n>? The problem is above I guess the ladder operator becomes some very ugly term. There should be a trick to compute <n|ξ^4|n>. Could anyone tell me?

Hello Physics Forum! I have a question: The problem: For a lightly damped oscillator being driven near resonance in the steady state, show that the fraction of its energy that is lost per cycle can be approximated by a constant (something like 2pi, which is to be determined) divided by the Q...

I've been trying to prove a rather simple looking concept. I have a code that calculates states of a 3D anisotropic oscillator in spherical coordinates. The spherical harmonics basis used to expand it's solutions in radial coordinate constraint the spectrum such that when the Hamiltonian is...

Hello, I am trying to get a better understanding of how oscillator circuits (clapp, hartley, colpitts etc) work, so I have been trying to solve the differential equation for a very simple one--the one most the way down the page here...

This isn't homework. I'm reviewing physics after many years of neglect. Since a simple harmonic oscillator is a conservative system with no energy losses, then a driven undamped harmonic oscillator, once the transient solution has died out, can't be receiving any energy from the driving...

Homework Statement A harmonic oscillator of mass m and angular frequency ω experiences the potential: V(x) = 1/2mω^{2}x^{2} between -infinity < x < +infinity and solving the schrodinger equation for this potential yields the energy levels E_n = (n + 1/2)...

Homework Statement The spin 1/2 electrons are placed in a one-dimensional harmonic oscillator potential of angular frequency ω. If a measurement of $$S_z$$ of the system returns $$\hbar$$. What is the smallest possible energy of the system? Homework Equations...

Homework Statement The Hamiltonian for the 3-D harmonic oscillator in spherical polar coordinates is given in the question.The question then asks : using the trial wavefunction ##ψ=e^(-αr) ## show that Homework Equations ##<ψ|H|ψ>/<ψ|ψ> = (\hbarα)^2/2m + 3mω^2/2α^2## The following...

(I am referring to section 3.1 in Burkhardt's "Foundations of Quantum Physics", if you happen to have the book.) In that book it's pointed out that the apparent contradiction between the pdf's of the QM ground state solution to the harmoinc oscillator with its classical conterpart (at the...

Hello Forum, The 1D harmonic oscillator is an important model of a system that oscillates periodically and sinusoidally about its equilibrium position. The restoring force is linear. There is only one mode with one single frequency omega_0 (which is the resonant frequency). What about the...

Dear kind helpers, actually I am not 100% sure whether this is the right place to post, as it is not a homework in the sense of an exercise sheet. But I think it could be because it feels pretty basic and that I should be able to solve it. Though I really searched for a solution but could not...

if we have two non-interacting particles of mass M in a one-dimensional harmonic oscillator potential of frequency ω, with the wavefunction defined as: $$\Psi\left(x_1,x_2\right) = \psi_n\left(x_1\right) \psi_m\left(x_2\right)$$ where x_1 and x_2 are two particle co-ordinates. and ψ_n is the...

Homework Statement The e-functions for n=0,1,2 e-energies are given as psi_0 = 1/(pi^1/4 * x0^1/2)*e^(x^2/(2*x0^2) psi_1 =... psi_2 =... The factor x0 is instantaneously changed to y= x0/2. This means the initial wavefunction does not change. Find the expansions coefficients of the...

[SIZE="4"]Definition/Summary An object (typically a "mass on a spring") which has a position (or the appropriate generalization of position) which varies sinusoidally in time. [SIZE="4"]Equations x(t)=A\sin(\omega t)+B\cos(\omega t) \omega^2 =\frac{k}{m} [SIZE="4"]Extended...

[SIZE="4"]Definition/Summary This is the quantum-mechanical version of the classical harmonic oscillator. Like the classical one, the quantum harmonic oscillator appears in several places, and it also appears in the quantization of fields. This article will discuss the one-dimensional...

I feel I understand what happens, and how to solve the equation of motion x(t) for a mass attached to a spring and released from rest horizontally on a smooth surface. We typically end up with x(t) = x_0 cos(ωt) as the solution, with x_0 as the amplitude of the oscillation. But I've...

Homework Statement A two-dimensional isotropic harmonic oscillator of mass μ has an energy of 2hω. It experiments a perturbation V = xy. What are its energies and eigenkets to first order? Homework Equations The energy operator / Hamiltonian: H = -h²/2μ(Px² + Py²) + μω(x² + y²) The...

I am working through Leonard Susskinds 'the theoretical minimum' and one of the exercises is to show that H=ω/2(p^2+q^2). The given equations are H=1/2mq(dot)^2 + k/2q^2, mq(dot)=p and ω^2=k/m. q is a generalisation of the space variable x, and (dot) is the time derivative if this helps...

Homework Statement Find the expectation values of x and p for the state \vert \alpha \rangle = e^{-\frac{1}{2}\vert\alpha\vert^2}exp(\alpha a^{\dagger})\vert 0 \rangle, where ##a## is the destruction operator. Homework Equations Destruction and creation operators ##a=Ax+Bp##...

Hi everyone, I have a rather fundamental question about building oscillator wavefunctions numerically. I'm using Matlab. Since it's 1/√(2nn!∏)*exp(-x2/2)*Hn(x), the normalization term tends to zero rapidly. So for very large N (N>=152 in Matlab) it is zero to machine precision! Though asymptotic...

A circuit is here. I built this circuit. People say a frequency is determined only by tank circuit and C2 is nothing to do with the frequency. But when i change C2 value, the output frequency changes. for example when C2 is 6pF 150Mhz, 12pF 120Mhz 18pF 108 Mhz. why is this happening? i'm...

Homework Statement For a particle of charge ##q## in a potential ##\frac{1}{2}m\omega^2x^2##, the wavefunction of ground state is given as ##\phi_0 = \left( \frac{m\omega }{\pi \hbar} \right)^{\frac{1}{4}} exp \left( -\frac{m\omega}{2\hbar} x^2 \right)##. Now an external electric field ##E##...

Homework Statement Homework Equations The Attempt at a Solution I find this task very hard to understand. First of all, when adding more mass, wouldn't that change the acceleration, according to F=ma? And in that case the velocity should also change when adding more mass, shouldn't it? That...

Let's say I have an anharmonic 1D oscillator that has the hamiltonian ##H=\frac{p^2}{2m}+\frac{1}{2}kx^2+\lambda x^4## or some other hamiltonian with higher than second-order terms in the potential energy. Is it possible, in general, to find raising and lowering operators for such a system? I...

I've attached a graph to this post. Why is it that the periodic external frequency applied never starts at 0 on graphs like these?

can someone please give me some information about electronic oscillator circuits, in particular pulse tone oscillators (thats what it says it is) consisting of a resistor and two capacitors. how does the resistance/capac effect frequency? what does the time constant have to do with it? does the...

Homework Statement In a port the tide and the low tide change with harmonic motion. at the high tide the water level is 12 meters and at the low tide it is 2 meters. between the tide and the low tide there are 6 hours. A ship needs 8 meters of water depth. how long can it stay in the port...

Homework Statement A mass of 0.1 kg has 2 springs of length 20 cm attached to each side, like in the drawing. they are loose. one has a constant of 50 [N/m] and the other 30. The system is between 2 walls 10 cm distant from each spring. At the second stage the springs are tied each to the...

hello! I have built a colpitts oscillator, but it is not producing a sine wave. the wiring diagram is attached. I used: L1= 1.066 millihenries L2= .142 millihenries R1= 10000Ω R2= 10000Ω C1= 470 microfarads C2= 680 microfarads for the transistor i just used a small npn. Tahnks!

Homework Statement Particle originally sits in ground state about x=0. Equilibrium is suddenly shifted to x=s. Find probability of particle being in new first excited state. Homework Equations The Attempt at a Solution Shifted wavefunctions are for ground state: ##\phi'_0 =...

Hello readers, Given the potential V(x) = - 1/ sqrt(1+x^2) I have found numerically 12 negative energy solutions Now I want to try to solve for these using matrix mechanics I know the matrix form of the harmonic oscillator operators X_ho, P_ho. I believe I need to perform the...

The energy changes correspond to infrared, h_bar * w. Which particles are actually oscillating? The neutrons or the electrons? Is it the electrons that fill up the stationary states, electronic configuration, or is it the nucleons that fill up the states?

A simple harmonic oscillator has total energy E= ½ K A^2 Where A is the amplitude of oscillation.  E= KE+PE a) Determine the kinetic and potential energies when the displacement is one half the amplitude. b) For what value of the displacement does the kinetic energy equal the potential...

Hi all, Im new here :-) So I am designing a simple Wien bridge oscillator, and need it to be set to a specific frequency. This is my circuit: Where C1 = C and C2 = C and R3 = R and R4 = R Im using ω=1/(C2R2) where C = my capacitor values and R = my Resistor values. My problem is, however...

Homework Statement 2N fermions of mass m are confined by the potential U(x)=1/2(k)(x2) (harmonic oscillator) What is the ground state energy of the system? Homework Equations V(x)=1/2m(ω2)(x2) The Attempt at a Solution I know the ground state energy of a simple harmonic...

Homework Statement Part (a): Derive Ehrenfest's Theorem. What is a good quantum number? Part (b): Write down the energy eigenvalues and sketch energy diagram showing first 6 levels. Part (c): What's the symmetry of the new system and what happens to energy levels? Find a new good quantum...

Homework Statement Consider a classical one-dimensional nonlinear oscillator whose energy is given by \epsilon=\frac{p^{2}}{2m}+ax^{4} where x,p, and m have their usual meanings; the paramater, a, is a constant a) If the oscillator is in equilibrium with a heat bath at temperature T...

In the course of solving the simple harmonic oscillator, one reaches a fork in the road. x(t) = A1Sin(wt) + A2Cos(wt) At this point, you exploit a trig identity and arrive at one of two solutions x(t) = B1Sin(wt+phi1) or x(t) = B2Cos(wt+phi2) Both of these are correct solutions...

My textbook says the ground state energy of the QSHO is given by 1/2*h_bar*w and that this is the minimum energy consistent with the uncertainty principle. However I am having trouble deriving this myself... ΔEΔt ≥ h_bar / 2.. so then ΔE/Δfrequency ≥ h_bar / 2... ΔE*2*pi / w ≥ h_bar / 2 ΔE ≥...

Hi folks! Apparently \Psi(x) = Ax^ne^{-m \omega x^2 / 2 \hbar} is an approximate solution to the harmonic oscillator in one dimension -\frac{\hbar ^2}{2m} \frac{d^2\psi}{dx^2} + \frac{1}{2}m \omega ^2 x^2 \psi = E \psi for sufficiently large values of |x|. I thought this...

Edit: Problem solved please disregard this post Homework Statement A particle in the harmonic oscillator potential has the initial wave function \Psi(x, 0) = ∑(from n = 0 to infinity) Cnψn(x) where the ψ(x) are the (normalized) harmonic oscillator eigenfunctions and the coefficients are given...

Homework Statement I found this in Binney's text, pg 154 where he described the radial probability density ##P_{(r)} \propto r^2 u_L## Homework Equations The Attempt at a Solution Isn't the radial probability density simply the square of the normalized wavefunction...

For oscillator wave function ##\frac{1}{\sqrt 2}(y-\frac{d}{dy})\psi_n(y)=\sqrt{n+1}\psi_{n+1}(y)## ##\frac{1}{\sqrt 2}(y+\frac{d}{dy})\psi_n(y)=\sqrt{n}\psi_{n-1}(y)## and I interpretate ##n## as number of phonons. Of course ##\psi_n(y)=C_ne^{-\frac{y^2}{2}}H_n(y)##. And ##C_n=f(n)##...

I'm trying to plot the evolution of a simple harmonic oscillator using MATLAB but I'm getting non-sense result and I have no idea what's wrong! Here's my code: clear clc x(1)=0; v(1)=10; h=.001; k=100; m=.1; t=[0:h:10]; n=length(t); for i=2:n F(i-1)=-k*x(i-1)...

Homework Statement A particle of mass m moves in a 1-D Harmonic oscillator potential with frequency \omega. The second excited state is \psi_{2}(x) = C(2 \alpha^{2} x^{2} + \lambda) e^{-\frac{1}{2} a^{2} x^{2}} with energy eigenvalue E_{2} = \frac{5}{2} \hbar \omega. C and \lambda are...

Homework Statement For the n = 1 harmonic oscillator wave function, find the probability p that, in an experiment which measures position, the particle will be found within a distance d = (mk)-1/4√ħ/2 of the origin. (Hint: Assume that the value of the integral α = ∫0^1/2 x^2e^(-x2/2) dx is...