1. NOTE: The spatial distribution depends on the particular frequencies involved
 x 2  1 k
k =
 x 
Two waves of slightly different wavelength and frequency produce beats.

3. Fourier Transforms
Generalization of ordinary “Fourier expansion” or “Fourier series”
Note how this pairs canonically conjugate variables  and t.

4. xk ~ 2
xp ~ h
t ~ 2
tE ~ h

5. 1896
1899
a, b g
1912

6. capable of penetrating thick opaque black paper aluminum plates
Henri Becquerel ( )
received the 1903 Nobel Prize
in Physics for the discovery
of natural radioactivity.
Wrapped photographic plate showed
clear silhouettes, when developed, of the
uranium salt samples stored atop it.
1896 While studying the photographic images of various fluorescent & phosphorescent
materials, Becquerel finds potassium-uranyl sulfate spontaneously emits radiation
capable of penetrating thick opaque black paper
aluminum plates
copper plates
Exhibited by all known compounds of uranium (phosphorescent or not)
and metallic uranium itself.

8. 1898 Marie Curie discovers thorium (90Th)
Together Pierre and Marie Curie discover
polonium (84Po) and radium (88Ra)
1899 Ernest Rutherford identifies 2 distinct kinds of rays
emitted by uranium
 - highly ionizing, but completely
absorbed by cm aluminum
foil or a few cm of air
 - less ionizing, but penetrate many
meters of air or up to a cm of
aluminum.
1900 P. Villard finds in addition to  rays, radium emits  - the least ionizing,
but capable of penetrating many cm of lead, several feet of concrete

9. a g b B-field points into page
Studying the deflection of these rays in magnetic fields,
Becquerel and the Curies establish  rays to be
charged particles