Find the integral.
## WarmUp Exercise #4, 8/30 (Assignment Due 9/4)

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

**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 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.

#### 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?**

**1) For the wave function to "revive"
or return to it's original state- it takes 1 unit-
meaning the same revival time for the ground state wave function of a particle in an infinite square
well.**

**2)For the probability density to repeat it takes .33
units or 1/3 of the revival time for the grounds state wave function of a particle in an
infinite square well.**

**3)As for thinking of a reason, I can't really.
For the first one, my only guess is that the amount of time it takes for the wave function is 1
because the time for the wave function to "revive" for the ground state is 1. So, because wave function 1 will only return to it's original state after 1
unit of time, if you superimpose another wave function on top of this it also will not go back to
it's original state until one unit of time is up.**

**As for the question 2, maybe it has something to do with frequency of probability changes= En1-En2/h, where En is dependent on n^2, So f is
proportional to 3, which means the revival time is 1/3 of the one in the ground state.**

**1. 1 full time unit**

**2. 0.33 time units**

**3. well, the revival time of the wave function is 3x the probability fn repeat time -- perhaps
this is because there are 3 n's total: one n=1
and one n=2. The prob density doesn't care which part of the wave function is where - just
cares about the square of the magnitude.**

**1. ~1**

**2. ~.3**

**3. Because the top diagram includes real and imaginary
energies and it takes longer to go through all the stages whist the probability is squared
and it repeats faster.**