Midterm tips & solution notes (Feb 23)

Midterm tip -1: Please occupy only every other seat starting with the seat closest to the aisle.

Midterm tips 0:  Plan to stay for the entire 1:45 minutes. With more time you can do more. Questions 5-7 are somewhat open-ended and you are invited to "go deep" on those. More thought, more nuance, in your responses is better. Additionally, sitting and concentrating for the whole time will help build your stamina for your 3 hour finals.

Problems1-4 are a total of 40 pts (8, 8, 10, 14)
Problems 5-7 are 20 pts each (expect to spend a lot of time on these).
8 is extra credit (about another 20 pts or so, also time consuming)

PS. In my opinion, adequate sleep, even a late morning nap, is helpful, especially when you will be ask to think and make connections.

Midterm tip #1: Include a graph!  
Whenever you are asked to write a paragraph about something, or to discuss or explain something: include a graph!  (or more than one graph if appropriate.) The graphs should, of course, be relevant and they should be referred to in your discussion. Labels on the axes are usually a good idea. Graphs and the discussion that accompanies them are an excellent way to get full credit and even extra credit. Even when you are not explicitly ask for a graph, please do include relevant graphs.

Midterm tip #2: Ignore extraneous information.
Sometimes you will be given extraneous information, information you do not need. That is to see if you can ferret out what is really important and essential to solve a particular problem. You are advised to trust your knowledge and preparation, and ignore extraneous information when the need arises.

Midterm tip #3: It helps if we all use the same states to start with. (The same notation.) For example, what I have for the 1DHO is:
$\psi_o (x) = (1/a \sqrt{\pi})^{1/2}e^{-x^2/(2a^2)}$

$\psi_1 (x) = (2/a \sqrt{\pi})^{1/2}(x/a)e^{-x^2/(2a^2)}$

$\psi_2 (x) = (2/a \sqrt{\pi})^{1/2}((x/a)^2-1/2)e^{-x^2/(2a^2)}$ 

Does that agree with what everyone else has and has been using? (These are discussed in an ancient video (from a December post, i think; the 2nd video made for this class) along with the corresponding infinite sq well states.)

Also, for the infinite square well centered at x=0, as requested below, i think the states are:
$\psi_o (x) = (2/L)^{1/2}cos (\pi x /L)$

$\psi_1 (x) = (2/L)^{1/2}sin (2 \pi x /L)$

$\psi_2 (x) = (2/L)^{1/2}cos (3 \pi x /L)$ 
================================

Solution notes for the midterm problems: