Oscillator Definition and 1000 Threads

I am unable to relate the Barkhausen criterion for oscillations to sustain to the Ideal LC oscillator with an initial condition. Assume you have a parallel combination of LC(both with Q=infinity) with an initial condition say V volts on capacitor. Mathematically it will oscillate with the...

Hello. I am trying to use the following equation: a\left|\psi_n\right\rangle=\sqrt{n}\left|\psi_{n-1}\right\rangle (where a is the "ladder operator"). What happens when I substitute \psi_n with \psi_0?

Homework Statement Hi, I'm currently studying for a quantum mechanics exam but I am stuck on a line in my notes: Ha\left|\Psi\right\rangle =\hbar\omega\left(a^{t}a a + \frac{a}{2}\right)\left|\Psi\right\rangleHa\left|\Psi\right\rangle =\hbar\omega\left(\left(a a^{t} - 1\right)a +...

Homework Statement Problem 8. 1. Express the distance x_c as a function of the mass m and the restoring parameter c used in Problem 7. (Problem 7. 1. Calculate the energy of a particle subject to the potential V(x) = V_0 + cx^2/2 if the particle is in the third excited state. 2...

The Hamiltonian of the diatomic molecule is given by H = p1^2 / 2m + p2^2 / 2m + 1/2 k R^2, where R equals the distance between atoms. Using this result, given in standard texbooks, I keep geting C = 9/2 kT instead of 7/2 kT for heat capacity. I've traced down my problem to the potential energy...

Hi, I have to find the 'stationary position' of a particle of mass m and charge q which moves in an isotropic 3D harmonic oscillator with natural frequency \omega_{0}, in a region containing a uniform electric field \boldsymbol{E} = E_{0}\hat{x} and a uniform magnetic field \boldsymbol{B} =...

Homework Statement The energy eigenvalues of an s-dimensional harmonic oscillator is: \epsilon_j = (j+\frac{s}{2})\hbar\omega show that the jth energy level has multiplicity \frac{(j + s - 1)!}{j!(s - 1)!} Homework Equations partition function: Z = \Sigma e^{-(...

given the Hamiltonian H=p^{2}- \omega x^{2} we can see inmediatly that this Hamiltonian will NOT have a BOUND state due to a 'saddle point' on (0,0) , here 'omega' is the frecuency of the Harmonic oscillations the classical solutions are not PERIODIC Asinh( \omega t) +Bcosh( \omega t)...

Hi, this is a fairly basic part of the whole coupled oscillators area, but I don't really get it. My problem is with the equations of motion of a coupled oscillator: F_A=-kx_A -2k'x_A and m\ddot x_A = -kx_A -k(x_A-x_B) Everywhere I've read seems to take it as intuitive, but I don't see...

Homework Statement A particle with mass m moves in the potential: V(x,y,z) = \frac{1}{2} k(x^{2}+y^{2}+z^{2}+ \lambda x y z) considering that lambda is low. a) Calculate the ground state energy accordingly to Pertubations Theory of the second order. b) Calculate the energies of...

Hey all, In the classical harmonic oscillator the force is given by Hooke's Law, F = -kx which gives us the potential energy function V(x)=(1/2)kx^2. Now I understand that the first derivative at the point of equilibrium must be zero since the slope at the point of equilibrium is zero. But what...

Homework Statement I am given the hamiltonian, where H^{^}_{0} is that of the harmonic oscillator and the perturbation is (lambda)*(h-bar)*(omega)*[(lowering operator)^2 + (raising operator)^2]. I am asked to find the ground state, second-order approx. energy value. Homework...

Is it better to use an op-amp oscillator or a crystal oscillator to produce 40 Khz sine wave?

Homework Statement Can someone please give me some hints how to solve this problem. Show that expected value for the kinetic energy is the same as the expected value for the potential energy for a harmonic oscillator in gound state. Homework Equations how to start with it? The...

Homework Statement A simple harmonic oscillator has amplitude 0.49 m and period 3.7 sec. What is the maximum acceleration? Homework Equations a(max)=Aw^2 w=angular frequency Vmax=Aw w= angular frequency The Attempt at a Solution I attempted to divide the Amplitude (.49m) by...

Homework Statement An electron is confined by the potential of a linear harmonic oscillator V(x)=1/2kx2 and subjected to a constant electric field E, parallel to the x-axis. a) Determine the variation in the electron’s energy levels caused by the electric field E. b) Show that the second order...

NOTE- Images are thumbnails, click to enlarge Homework Statement Show that the positive feedback gain expression for the circuit below is v2/v0 = 1/[3 + j(wL/R - R/WL)] (anything in red I added to the original problem) Homework Equations (above)The Attempt at a Solution Along with the below...

Cant oscillate sine wave from "bubba" oscillator hey i can't oscillate sine wave from "bubba" oscillator using pSpice. see the following attachment. can u please help me?

Homework Statement What is the phase constant (from 0 to 2π rad) for the harmonic oscillator with the velocity function v(t) given in Fig. 15-30 if the position function x(t) has the form x = xmcos(ωt + φ)? The vertical axis scale is set by vs = 7.50 cm/s...

Homework Statement I need to find <x>, <x2>, <p>, and <p2> for a particle in the first state of a harmonic oscillator. Homework Equations The harmonic oscillator in the first state is described by \psi(x)=A\alpha1/2*x*e-\alpha*x2/2. I'm using the definition <Q>=(\int\psi1*Q*\psi)dx...

Homework Statement Consider the CO2 molecule as a system made of a central mass m_2 connected by equal springs of spring constant k to two masses m_1 and m_3 a) set up and solve the equations for the two normal modes in which the masses oscillate along the line joining their centers (the...

Homework Statement Two identical undamped oscillators are coupled in such a way that the coupling force exerted on oscillator A is \alpha\frac{d^2x_a}{dt^2} and the coupling force exerted on oscillator B is \alpha\frac{d^2x_b}{dt^2} where \alpha is a coupling constant with magnitude less than...

I'm looking at a question... The last part is this: find the expectation values of energy at t=0 The function that describes the particle of mass m is A.SUM[(1/sqrt2)^n].\varphi_n where I've found A to be 1/sqrt2. The energy eigenstates are \varphi_n with eigenvalue E_n=(n + 1/2)hw...

Homework Statement An oscillator circuit is important to many applications. A simple oscillator circuit can be built by adding a neon gas tube to an RC circuit, as shown in the figure below. Gas is normally a good insulator, and the resistance of the gas tube is essentially infinite when the...

Quantum Harmonic Oscillator Operator Commution (solved) EDIT This was solved thanks to CompuChip! The entire post is also not very interesting as it was a basic mistake :P No need to waste time This is not homework (I am not currently in college :P), but it is a mathematical question I'm...

Ok, so I am trying understand how to derive the following version of the Schrodinger Equation for QHO: \frac{d^2u}{dz^2} + (2\epsilon-z^2)u=0 where \ 1. z=(\frac{m\omega}{hbar})^{1/2}x and \ 2. \epsilon= \frac{E}{hbar\omega} I've started with the TISE, used a potential of...

Homework Statement This is for my mechanics class. It seems like it should be easier than I'm making it. A single object of mass m is attached to the ends of two identical, very long springs of spring constant k. One spring is lined up on the x-axis; the other on the y-axis. Chpose your...

Homework Statement Consider a harmonic oscillator with mass=0.1kg, k=50N/m , h-bar=1.055x10-34 Let this oscillator have the same energy as a mass on a spring, with the same k and m, released from rest at a displacement of 5.00 cm from equilibrium. What is the quantum number n of the state of...

Hi, so I did the question, but apparently my answer is off by a factor of 2. An accelerated electron radiates energy at the rate Ke2a2/c3...e is the electron charge, a is the instantaneous acceleration, c is the speed of light, K=6x109Nm2/C2...whatever that is. So first I had to find how much...

An experimenter has carefully prepared a particle of mass m in the first excited state of a one dimensional harmonic oscillator. Suddenly he coughs and knocks the center of the potential a small distance, a, to one side. It takes him a time T to recover and when he has done so he immediately...

This is not really homework, just a project I'm toying with in my sparetime. I'm doing some Path Integral Monte Carlo simulations, for now just for the 1D quantum harmonic oscillator. Anyways, currently I compare my results to the analytic mean energy of a 1D quantum harmonic oscillator, given...

Find the time dependence of the expectation value <x> in a quantum harmonic oscillator, where the potential is given by V=\frac{1}{2}kx^2 I'm assuming some wavefunction of the form \Psi(x,t)=\psi(x) e^{-iEt/\hbar} When I apply the position operator, I get: <x>=\int_{-\infty}^\infty...

How do you use the C_ij matrix to find the harmonic frequency (or frequencies) of a diatomic molecule, the OH (hydroxyl) radical? (I have no idea how to set it up for this.) This is from Feynmann's book on Statistical Mechanics...

how to design an oscillator to produce an output frequency at 950MHz and amplitude +/- 3 Volt.

Homework Statement V(x) = \frac{1}{2}mw^{2}x^{2} + \lambdax^{4} Using first-order perturbation theory to calculate the energy shift of: 1. The ground state: \psi_{0}(x) = (2\pi\sigma)^{\frac{-1}{4}}\exp(\frac{-x^{2}}{4\sigma}) of the harmonic oscillator, where...

hey, i need help in solving the equation of a mathieu oscillator (ignoring damping) and showing how the condition for max parametric resonance is doubling of the natural frequency . ( got viva 2morro. I am so going to suck) D^2x + K(t)x =0 (Ko is the constant natural frequency when no...

I am having to ask this from lack of electronic components in my area, so, I want to ask if it is possible to make an AM transmitter (short range) using a clock oscillator? I believe it might be possible, but as the crystal is 32768 Hz, it makes sense to ask, what kind of receiver set should I...

Homework Statement P4-1. The Method of Frobenius: Sines and Cosines. The solutions to the differential equation y"+ y = 0 can be expressed in terms of our familiar sine and cosine: y(x) = Acos(x) + Bsin(x) . Use the Method of Frobenius to solve the above differential equation for the even...

I Have a brief idea about the equation and i have searched the web for its application to one dimensional harmonic oscillator but no use. Any Help Would Be Welcomed Especially about the latter:smile:

Homework Statement I have an assignment to make a C++ program (I've never seen C++ before, and my professor has never taught it) that makes a set of displacement values corresponding to the motion of a damped oscillator. The function is: x = A*e^{(-\gamma*t/2)} * cos(\omega*t) where...

hi i have no idea how to do it, can some one give me a direction or an outline? A 1.05 kg mass is suspended from a spring, with a spring constant of 161.0 N/m. Find the driving frequency which would cause resonance. all i need is to know where to start from

Homework Statement I have a simple harmonic oscillator system with the driving force a sinusoidal term. The question is to find the general solution and the amplitude of the steady state solution Homework Equations I found the steady state part of the solution. It is of the form...

Homework Statement Consider a damped oscillator, with natural frequency \omega_{o} and damping constant B, both fixed, that is driven by force F(t) = F_{o}cos(\omegat). Verify that the average rate at which energy is lost to the resistive force is mB\omega^2A^2. Homework Equations x =...

I know that the HO hamiltonian in matrix form using the known eigenvalues is <i|H|j> = E^j * delta_ij = (j+1/2)hbar*omega*delta_ij, a diagonalized matrix. How do I set up the non-diagonalized matrix from the potential V=1/2kx^2?

Homework Statement Does a wavefunction have to be normalized before you can calculate the probability density? Homework Equations n/a The Attempt at a Solution Im thinking yes? so that your probability will be in between 0 and 1?

Homework Statement Find the frequency that gives the maximum amplitude response for the forced damped oscillator d^{2}x/dt^{2} + 6dx/dt + 45x = 50cos(\omegat) Homework Equations I'm really confused by this problem, but I know that the amplitude can be found by taking the...

hello friends, in my course "introductory QM" it says at the end of harmonic oscillator chapter that this may find some applicasions in electromagnetic fields and in crystal physics. now, though i haven't covered solid state physics yet, but still i can...

Are there sine wave generators for current? I need something like .1Hz, 30uA_rms, to a target of about 1kOhm. If you would try to convert a normal function generator for this purpose, would you go for a large resistance like 1MOhm in series or a current mirror design? Where would the noise be...

Homework Statement Calculate the ratio of the kinetic energy to the potential energy of a simple harmonic oscillator when its displacement is half its amplitude. Homework Equations KE=1/2mv2 = 1/2kA2sin2(wt) U=1/2kx2 = 1/2kA2cos2(wt) KEmax=1/2kA2 Umax=1/2KA2 The Attempt at a...

Homework Statement Consider a particle of mass m moving in a one-dimensional potential, V(x)=\infty for x\leq0 V(x)=\frac{1}{2}m{\omega^2}{x^2} for x>0 This potential describes an elastic spring (with spring constant K = m\omega^2) that can be extended but not compressed. By...