Classical and Quantum Particle in a Harmonic Oscillator
## Classical / Quantum Exercise #3

#### Please answer the following 2 questions
regarding the Physlet:

#### 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.