Classical and Quantum Particle in a Harmonic Oscillator

## Classical / Quantum Exercise #3

 1 < N < 10 Start Classical Graph Start Quantum Graph

#### Description

The graphs above show the quantum and classical representations of the position of a particle constrained to undergo motion subject to a gravitational force before hitting a hard wall or table at x=0 (note: this representation is a 90 degree rotation of the usual problem).  The classical mechanical representation of the position of the particle is on the left.  The quantum mechanical representation of the position of a particle is on the right.

#### Questions

1. Click on "Start Quantum Graph" below the right-hand graph.  The graph shows the probability that a particle is in the ground state at some position x.  You may vary n to see higher energy states.  Under the left-hand graph, a ball is subjected to the force of gravity---shown with the force of gravity to the left---and bounces on a hard surface at x=0.  What does the probability of finding the particle as a function of x look like?   Why?  After you answer, click "start Classical Graph" and check yourself.  Was your answer right or wrong?

2. Under what conditions would the right-hand graph look like the left-hand graph.  In other words, what is the correspondence between the classical and quantum position probabilities of a particle undergoing simple harmonic motion?  Check your answer using the above "Start" buttons.

#### Credits

Script by Mario Belloni and Wolfgang Christian.
Questions by Larry Cain.
Java applets by Wolfgang Christian.