Modern 2:Exam 1 Overview
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* lots of people messed up exponents when doing division. <math>10^9 / 10^{-9} = 10^{18} </math> | * lots of people messed up exponents when doing division. <math>10^9 / 10^{-9} = 10^{18} </math> | ||
* break up complicated numerical factors involving multiplications and divisions into small pieces. First do the numerator, then do the denominator and then get your final estimate. | * break up complicated numerical factors involving multiplications and divisions into small pieces. First do the numerator, then do the denominator and then get your final estimate. | ||
| − | * lots of people messed up: <math> |e^{I k x}|^2 </math>. This is 1! | + | * lots of people messed up: <math> |e^{I k x}|^2 </math>. This is 1! |
| + | * some people used <math> |e^{I k_0 x}|^2 </math> and some used <math> |e^{I -k_0 x}|^2 </math>. | ||
| + | I didn't take off for this. But it does change the sign of the momentum. | ||
| + | * A Gaussian <math>e^{(x-x_0)^2/2\sigma^2}</math> is centered at <math>x_0</math>. You '''can''' | ||
| + | show this by integration, but it should be sufficiently well known that you merely state it as | ||
| + | a fact. | ||
Revision as of 16:42, 6 March 2006
tips and tricks
- I don't expect exactitude in numerical calculations. So as far as I'm
concerned 1.9 = 3 and π = 3 so 1.9π = 6
- lots of people messed up exponents when doing division. 109 / 10 − 9 = 1018
- break up complicated numerical factors involving multiplications and divisions into small pieces. First do the numerator, then do the denominator and then get your final estimate.
- lots of people messed up: | eIkx | 2. This is 1!
- some people used
and some used 
.
I didn't take off for this. But it does change the sign of the momentum.
- A Gaussian
is centered at x0. You can
show this by integration, but it should be sufficiently well known that you merely state it as a fact.
