Here is the HOMEWORK for this week

2a and b) (Although you might find it instructive to try) you really do not have to REDO any of the hairy integrals Gas has done for you already! Just think about how you invert Fourier Transforms (be sure to get the factors of 2 Pi right) and think about simple variable changes, and you should be able to find the answer without doing any new integrals. (In fact, with a little thought you might even be able to just guess the answers)

3) Gas. has a bad typo in his constants, the electron mass is 9.1*10^-28 g.

(You can ignore his hint about how to express widths if you want!)

Also, Gas' formula for the width has a mistake in it, I claim:

(we disagree about that factor of 4 in the denominator in the 1st line)

I get very large numbers for part a (fractional changes of over 10 million and over 10^15!), and a tiny number for part b.

4a) See #3. (I get a width between 10 and 100 cm in part a).

For part b:

Think about what happens if a particle gets VERY relativistic! I get a width essentially unchanged in part b, do you see why?

5) For the ground state, convince yourself that the uncertainty in x ( or p) is roughly equal in magnitude to a typical value of x ( or p) (Can you explain briefly why this is?) The uncertainty principle then relates x and p, so you can eliminate either from the energy equation. (To find the lowest energy, you can differentiate w.r.t. the remaining variable and set to 0... )

6) Think a bit about relating Delta E to Delta lambda. (If E=hc/lambda, it is NOT true that Delta E = hc/[Delta lambda]!!)

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Go to the Physics Department's home page.