## Time Evolution Exercise #2

#### Please answer the following 3 questions
regarding the Physlet:

#### Description

The superposition shown---both Y_{n1n2}
and Y_{n1n2}^{*}Y_{n1n2}---is
an equal mix of the two states n_{1 }and n_{2 }for the infinite
square well, Y_{n1n2}(x,t)=(1/2)^{-1/2
}[f_{n1} (x,t) + f_{n2}
(x,t)]. The wave function evolves with time according to the TDSE. You may
change the state by choosing an n_{1} and n_{2}. 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. ** Restart.**

#### Questions

- For n
_{1}=1 and n_{2}=2, how long does it take for the
wave function to revive?
- For n
_{1}=1 and n_{2}=2, how long does it take for the
probability density to repeat?
- 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).

*© Copyright 2003 Mario Belloni and Wolfgang Christian.*