HW 5 solutions.

Enclosed are HW 5 solutions. Problems 1-3 provide an opportunity to understand confinement and its consequences. $\Delta x$ reflects the value of x^2, not x, in our problems; this is a measure of confinement. Similarly, $\Delta p$ reflects the value of p^2, not p, and is proportional to kinetic energy. Thus it is natural and probably less subject to misinterpretation to recast the "uncertainty" relationship, as we did, as a relationship between confinement and kinetic energy.

I believe that some people found problem 4 to be a little tricky or confusing. My approach to problem 4 is on the last page. For the HO GS you start with kinetic energy as a function of a. And we also have a relationship between a and $\Delta x$. You can use that to substitute out a and get a relationship between T and $\Delta x$ for this particular case. For the Inf sq well case, you start with kinetic energy as a function of L.  You also have a relationship between L and $\Delta x$ which you can use that to substitute out L and get a relationship between T and $\Delta x$ for this particular case.

Though I won't discuss the integrands of 5-7 here, they are quite important. Feel free to post any questions or comments about them here.

Problem 8 provides an example of a state for which the confinement of the electron changes fairly dramatically as a function of time. I think the KE will also vary in a complementary manner. That is, It will be largest when the wave-function is most confined as oscillate as a function of time, like x^2, but 180 degrees out of phase.