1d harmonic oscillator Definition and 14 Threads

hi guys i am trying to solve the Asymptotic differential equation of the Quantum Harmonic oscillator using power series method and i am kinda stuck : $$y'' = (x^{2}-ε)y$$ the asymptotic equation becomes : $$y'' ≈ x^{2}y$$ using the power series method ##y(x) = \sum_{0}^{∞} a_{n}x^{n}## , this...

I have got a simple qstion. We have a particle in 1d oscillator with E0( fundamental level).We know that phi~ e^-x^2 for any x, so We can measure a position and get a value x=a, such that V(a)>E0 . In this case T<0 so the velocity of the particle is imaginary, how is this even possible?, (a real...

Homework Statement Show that for the one-dimensional linear harmonic oscillator the Hamiltonian is: [; H = \frac{1}{2}[P^2+\omega ^2 X^2]-\frac{1}{2}\omega \hbar ;] [; =\frac{1}{2}[P+i\omega X][P-i\omega X]+\frac{1}{2} \omega \hbar ;] where P, X are the momentum and position operators...

The ground state wave-function of a 1-D harmonic oscillator is $$ \psi(x) = \sqrt\frac{a}{\sqrt\pi} * exp(-\frac{a^2*x^2}{2}\frac{i\omega t}{2}). $$ a) find Average potential energy ? $$ \overline{V} = \frac{1}{2} \mu\omega^2\overline{x^2} $$ b) find Average kinetic energy ? $$ \overline{T} =...

Hey, I'm stuck halfway through the solution it seems. I could use some tips on how to continue. 1. Homework Statement I have to determine a linear combination of the states |0\rangle, |1\rangle, of a one dimensional harmonic oscillator, so that the expectation value \langle x \rangle is a...

Homework Statement Hello, I'm just curious as to whether I'm going about solving the following problem correctly... Problem Statement: A particle mass m and charge q is in the ground state of a one -dimensional harmonic oscillator, the oscillator frequency is ω_o. An electric field ε_o is...

Hi. I want to write the entropy of a 1d harmonic oscillator as a function of energy, but for each energy there is only one possible configuration. So is the entropy zero? I mean, the energy is E=hw(n+1/2), so there is only one microstate for each energy.

Hi, I'm currently working through some exam papers from previous years before an upcoming module in Quantum Mechanics. Homework Statement See the attached image Homework Equations The Attempt at a Solution I'm a little stumped with this one, I'm assuming that I'm looking...

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 Find the eigenvalues and eigenfunctions of H\hat{} for a 1D harmonic oscillator system with V(x) = infinity for x<0, V(x) = 1/2kx^2 for x > or equal to 0. Homework Equations The Attempt at a Solution I think the hamiltonian is equal to the potential + kinetic...

Homework Statement "Two non-interacting particles are placed in a one-dimensional harmonic oscillator potential. What are the degeneracies of the two lowest energy states of the system if the particles are a)identical spinless bosons b)identical spin-1/2 fermions? Homework Equations...

Hi. I have recently designed a simulator about Qunatum Mechanics one dimensional harmonic oscillator. Please try it. I will be glad to read your opinions. http://erham.persiangig.ir/Programs/1386/QM1DHOS10.png Size: 223 KB http://erham.persiangig.ir/Programs/1386/QM1DHOS10.zip"

Homework Statement particle in ground state of 1D harmonic oscillator - spring constant is doubled - what is the probability of finding the particle in the ground state of the new potential Homework Equations v=1/2kx^2 oscillator potential wavefunction ground state n=0 =...