Two waves of slightly different wavelength and frequency produce beats.

x

x

1k

k = 2

NOTE: The spatial distribution depends on the particular frequencies involved

Fourier Transforms Generalization of ordinary “Fourier expansion” or “Fourier series”

de)(g2

1)t(f ti

de)t(f2

1)(g ti

Note how this pairs canonically conjugate variables and t.

xk ~ 2

t ~ 2

xp ~ h

tE ~ h

1896

1899

1912

Henri Becquerel (1852-1908) 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.

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 0.006 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

B-fieldpoints

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1900-01 Studying the deflection of these rays in magnetic fields, Becquerel and the Curies establish rays to be charged particles