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