Eigenvalue5

Expectation Value Problem #1

 Choose a Level = , then

Description

This is an introductory question related to expectation values and the Heisenberg Uncertainty Principle.

Questions

A particle is in a one-dimensional dimensionless harmonic oscillator potential

[ - (d/dx)2 + x2 ] Psi = E Psi.

The states shown are normalized.  Shown is Psi and the results of the integrals that give <x> and <x2> <p> and <p2> (which are by convention are unitless).  Vary n from 1 to 10. 

  1. In this dimensionless case, hbar=1.  What other constants---or group of constants---must be set equal to one? 

  2. What do you notice about <x> and <x2> and <p> and <p2>? 

  3. Calculate DxDp for n=0.  What do you notice considering hbar=1?

  4. What is En?  How does this agree with or disagreee with the standard case for the harmonic oscillator? 

  5. How much KE and how much PE?

Credits

Script by Mario Belloni.
Questions by Mario Belloni.
Java applets by Wolfgang Christian.