Quantum-mechanical Superposition Exercises

 

Harmonic Oscillator shows the first five energy eigenstates and six two-state superpositions for a particle in a harmonic oscillator.  The eigenstates are shown in position and momentum space.  The two-state superpositions are time dependent and are shown to evolve in time.  The superpositions are shown in position and momentum space.  In addition, one can choose to look at the expectation value of x and p.

 

~~1. Describe how the energy eigenstates (both position and momentum space) change as n increases.  What are <x> and <p> for t = 0?  Does the probability density, <x>, or <p> change over time for the energy eigenstates? 

 

~~2. Describe how the two-state superpositions (both position and momentum space) change as n increases.  What are <x> and <p> for t = 0?  Does the probability density, <x>, or <p> change over time for these superpositons?