1
BACKGROUND QUANTUM PHYSICS 19001925
In these notes we briefly discuss several of the important developments in quantum physics in the period 19001925
before the invention of quantum mechanics by Heisenberg and Schrodinger [1, 2].
•
Blackbody radiation (Planck 1900)
Consider the electromagnetic radiation inside a cavity with walls at temperature
T
, see Fig.1 . The energy is distributed
across the frequency spectrum. Let
U
(
ν
)
dν
be the energy of radiation between frequency
ν
and
ν
+
dν
. Based on
thermodynamics Wien predicted
U
(
ν
) =
ν
3
f
(
ν/T
) where
f
is an unknown function.
(
( )
I
U
Q
Q
, v
FIG. 1. The intensity of light emitted at frequency
ν
is proportional to the corresponding energy density per unit frequency
interval
U
(
ν
) in the cavity of volume
V
.
Using classical elecromagnetic theory Rayleigh and Jeans found
U
(
ν
) = (8
πV/c
3
)
ν
2
kT
; at high frequencies this
diverges as does the total energy
integraltext
∞
0
U
(
ν
)
dν
. Wien fitted the measured distribution to the function
U
(
ν
)
∝
ν
3
e
−
pν/
(
kT
)
where
k
is Boltzmann’s constant and
p
is a numerically fitted parameter, though the fit was not very good. Planck
obtained a perfect fit, within experimental error, to the measured spectrum with the function
U
(
ν
) =
8
πV
c
3
hν
3
1
e
hν/
(
kT
)

1
.
The fitting parameter
h
= 6
.
6
×
10
−
34
Js is Planck’s constant. (Note:
hν
=
planckover2pi1
ω
where
planckover2pi1
=
h/
(2
π
) and
ω
= 2
πν
.) Note
that Planck’s law agrees with Wien’s law. Moreover it agrees with classical physics ( in the guise of the RayleighJeans
law ) when
kT >> hν
(check it). Planck introduced the revolutionary “quantum hypothesis” that energy is emitted
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 Fall '10
 Kennedy
 mechanics, Quantum Physics, Photon, Radiation, Planck, Broglie wavelength

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