Quantum harmonic oscillator Definition and 110 Threads

Homework Statement Hi, Could someone give me a tip or two for how to calculate the mean square position ( <x^2>) for a linear quantum harmonic oscillator? Homework Equations I think I'm supposed to use the following recursion relation for Hermite polynomials: yHv=vHv-1 + .5Hv+1 the...

Thanks in advance for reading/replying Homework Statement In the interval (t+dt, t) the Hamiltonian H of some system varies in such a way that |H|psi>| remains finite. Show that under these circumstances |psi> is a continuous function of time. A harmonic oscillator with frequency w is in...

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 H = p^2/2m + (kx^2)/2 - qAx (THis is a harmonic potentional with external electric force in 1D) Braket: Definitions: |0, A=0 > = |0>_0 for t=0 (ground state) |0, A not 0 > = |0> for t=0 (ground state) 2. Question 1. Find the probability of being in the state |0, A...

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...

Homework Statement Is there any way to find <\varphi_{n}(x)|x|\varphi_{m}(x)|> (where phi_n(x) , phi_m(x) are eigenfunction of harmonic oscillator) without doing integral ? Homework Equations perhaps orthonormality of hermite polynomials ...

looking at the quantum mechanical harmonic oscillator, one has the differential equation in the form: \frac{d^2\psi}{du^2}+(\alpha-u^2)\psi=0 when a person who doesn't know any physics sees the equation, he will try a serial solution for psi, and he will find a solution with some recursive...

Can someone explain to me how they went from U(x)=(1/2)kx^2 to E=(n+1/2)(h/2pi)w? http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc.html

Hi, Is there an explicit formula for the eigenfunctions of the harmonic oscillator? By explicit, I mean "not written as the nth power of the operator (ax-d/dx) acting on the ground state". Thanks.

Hi, I am wondering how i would go about calculating the canonical partition function for a system of N quantum harmonic oscillators. The idea of the question is that we are treating photons as oscillators with a discrete energy spectrum. I'm confused as whether to use Maxwell-Boltmann...