Simple harmonic oscillator Definition and 109 Threads

[SOLVED] Perturbation of the simple harmonic oscillator Homework Statement An additional term V0e-ax2 is added to the potential of the simple harmonic oscillator (V and a are constants, V is small, a>0). Calculate the first-order correction of the ground state. How does the correction change...

[SOLVED] QM simple harmonic oscillator Homework Statement If I have a particle in an SHO potential and an electric field, I can represent its potential as: V(x) = 0.5 * m \omega^2 (x - \frac{qE}{mw^2})^2 - \frac{1}{2m}(\frac{qE}{\omega})^2 I know the solutions to the TISE...

I was just wondering what the difference was in the 1-D simple harmonic oscillator in the Heisenberg picture versus the Schrodinger picture?

The problem is the following: a.) Obtain the equation of motion for the very small oscillations of a bead of mass m attached 1/5th of the way along a massless string of length 5l, which is under tension T. b.) Hence show that the angular frequency of oscillation is omega=sqrt(5T/4ml)...

Hi, I've been scouring through many textbooks to try find some kind of solution to a question I have been asked for a problem sheet and was wondering if any1 would be able to help. The question is as follows; The simple harmonic oscillator with hamiltonian H = (p^2/2m) + (1/2(mw^2x^2) is...

For some reason this problem has me stuck. It isn't homework, but it might be on the exam Tommorrow. If anyone is still awake, please steer me in the right direction. Thank you A simple harmonic oscillator has a total energy of E. (a) determine the kinetic and potential energies when...

a damped simple harmonic oscillator has mass m = 260 g, k = 95 N/m, and b = 75 g/s. Assume all other components have negligible mass. What is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles (Adamped / Ainitial)? having trouble getting...

In my mechanics textbook is given an exemple of how to find the general solution of the of the equation of motion for a force -kx (the simple harmonic oscillator problem). He begin his analysis and finds that e^(iwt) and e^(-iwt) are both solutions. Hence C1*e^(iwt) and C2*e^(-iwt) are also...

If the universe is a simple harmonic oscillator then it must be symmetrical and divided into two halves , each half with approximately 10^52 kg of mass at its centre of mass. If the universe reaches about 10^26 metres in about 10^18.5 seconds then using E = ( n + 1/2)h w for an oscillator we...