Please answer the following 6 questions
regarding the Physlet:

Description

The superposition shown---both Y_{n1n2}
and Y_{n1n2}^{* }x^{ }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 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 ground state wave
function to undergo a phase change of 2p.

Questions

Vary n_{1} and n_{2} keeping n_{1}<n_{2}
to avoid double counting and also avoid n_{1}=n_{2}. Vary
the quantum numbers from 1 to 10.

For n_{1} = 1 n_{2} = 2, what is Dp
at t=0?

For n_{1} = 1 n_{2} = 2, what is Dp
at t=0.083 (1/12)?

For n_{1} = 1 n_{2} = 2, what is Dp
at t=0.166 (1/6)?

For n_{1} = 1 n_{2} = 2, what is Dp
at t=0.250 (1/4)?

For n_{1} = 1 n_{2} = 2, what is Dp
at t=0.333 (1/3)?

What do you recognize from this pattern and by looking at the wave
function?

Credits

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