3 7 8 D O C . 3 8 5 Q U A N T U M T H E O R Y O F I D E A L G A S I I
How a material particle, or a system of material particles, can be assigned a (sca-
lar) field of waves has been demonstrated by Mr. E. de Broglie in a very noteworthy
paper.*)
A material particle of mass m is first assigned a frequency ν according to
the equation
(35)
Now let the particle be at rest with reference to a Galilean system K′, in which we
imagine a synchronous oscillation of the frequency ν0 everywhere. Relative to a
system K, with reference to which K′ is moving with mass m at the velocity v along
the (positive) X axis, there then exists a wavelike process of the type
Frequency ν and phase velocity V of this process are hence given by
(36)
(37)
ν is then—as Mr. De Broglie has shown—at the same time the group velocity of
this wave. It is furthermore interesting that, according to (35) and (36), the parti-
cle’s energy is exactly equal to hν, in concordance with the fundamental
relation of quantum theory.
One then sees that to such a gas a scalar wave field can be assigned, and I have
become persuaded by calculation that [14] is the mean square of the fluctuation
*)
Louis de Broglie. Thèses. Paris (Edit. Musson & Co.), 1924. There is a very remarkable
geometrical interpretation of the Bohr-Sommerfeld quantum rule in this dissertation as
well.[13]
mc2
hν0. =
2πν0------------------¸
t
v
c2
----x - –
1
v2¸
c2
----¹ -–
©
¨
¨ ¸
§ ·
. sin¨
ν
ν0
1
v2
c2
---- -–
------------------ =
V
c2
v
---- -=
[p. 10]
mc2
1
v2
c2
---- -–
------------------
1
Zν
-----