Classical and Quantum Particle in a Harmonic Oscillator

Classical / Quantum Exercise #2

Please answer the  following 2 questions regarding the Physlet:

N =              0<N<25

Start Classical Graph  Start Quantum Graph

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 oscillating back and forth on a spring.  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.