Here is the HOMEWORK for this week

1) is normalized. Use the "completeness" trick, it's the niftiest proof! (Gas does the proof *without* using Dirac notation after Eq 6-22)

b) See e.g. Gas Eq 6-14 and 6-15. An example of "completeness" for continuous variables is found e.g. in Gas eqs 7-43 and 7-45.

2) I get a probability between 60 and 70%. (My answer is exact, and is best expressed as a fraction)

3b) What is for a stationary state? What is ? (There are various tricks to see the latter, e.g. look at Gas 6-72, and think about the time dependence of <x> in a stationary state...)

4) Use Gas. 6-68. (Can you combine the eqns for d<x>/dt and d<p>/dt to get a simple second order diff.eq. you can solve immediately for <x>(t)?)

5a) Like in the hint above, think about the TIME dependence of <x p> in a stationary state.

b) Remember the classical limit of Ehrenfests theorem was Newton's 2nd law, because

c) The first should tell you something very familiar (see e.g. Eqn. 3-13)

The second is also something very intuitive. Just state it in words.