Homework 4 solutions: how the hydrogen atom gets its size.

The enclosed are some solutions for HW 4.  I melded problems 6 and 8 together in the solutions, although you were not required to do that. That problem shows how the electron's (ground state) wave-function in a hydrogen atom "decided" that 0.053 nm was just the right size. Sort of like Goldilocks, it "realized" that if its size were larger then it would not have a large enough potential energy, while if it were smaller (more confined to the region around the proton), then its kinetic energy would be too high. So that is how the hydrogen atom got its size. 

It is the last part that is uniquely quantum, and an example of how the nature of quantum KE, which is unusual, influences many basic phenomena. 

One side note on problem 9: I don't know if anyone did that problem. I had meant to make the state fr that problem and equal mix of $Psi_o$ and $Psi_2$, which I am pretty sure has a lot of time dependence for T and U because that mixed state "expands" and "contracts" quite a bit as a function of time. Calculating x^2 for that mixed state is now on HW 5 as an advanced problem; it is pretty interesting I think.

Please feel free to post comments and questions and initiate discussion here. Hope fully these are interesting and stimulating topics.