« · »

Physlets run in a Java-enabled browser, except Chrome, on the latest Windows & Mac operating systems. If Physlets do not run, click here for help updating Java & setting Java security.

Problem 12.2: A particle is in a 1-d dimensionless harmonic oscillator potential

Choose a Level = , then

Please wait for the animation to completely load.

A particle is in a one-dimensional harmonic oscillator potential (ħ = 2m = 1; ω = k = 2). The states shown are normalized. Shown are ψ and the results of the integrals that give <x> and <x2> and <p> and <p2>.  Vary n from 1 to 10.

  1. What do you notice about how <x> and <x2> and <p> and <p2> change?
  2. Calculate ΔxΔp for n = 0. What do you notice considering ħ = 1?
  3. What is En?  How does this agree with or disagree with the standard case for the harmonic oscillator?
  4. How much average kinetic and potential energies are in an arbitrary energy state?
The OSP Network:
Open Source Physics - Tracker - EJS Modeling
Physlet Physics
Physlet Quantum Physics