Time Evolution Exercise #2

Please answer the  following 3 questions regarding the Physlet:

n1 =       n2 =    
Start =             End =
 

Description

The superposition shown---both Yn1n2 and Yn1n2*Yn1n2---is an equal mix of the two states n1 and n2 for the infinite square well, Yn1n2(x,t)=(1/2)-1/2 [fn1 (x,t) + fn2 (x,t)].  The wave function evolves with time according to the TDSE.  You may change the state by choosing an n1 and n2.  Time is shown in units of the revival time for the ground state wave function of a particle in an infinite square well.  In other words it is the time for the wave function to undergo a phase change of 2p

Questions

  1. For n1=1 and n2=2, how long does it take for the wave function to revive?
  2. For n1=1 and n2=2, how long does it take for the probability density to repeat?
  3. Can you think of a reason for your results in questions 1 and 2?

References

D.F. Styer, "Quantum Revivals Versus Classical Periodicity in the Infinite Square Well," Am. J. Phys. 69, 56-62 (2001).

Credits

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