1 4 2 D O C U M E N T 1 4 8 N O V E M B E R 1 9 2 3
[Now] if suitable rays are offered to an atom at the velocity in the –x direction
and are reemitted by it in the –x direction, then the atom later has the velocity
, where . Hence the radiation gains the energy[1]
Thereby is the radiation’s gain in frequency because the Doppler part of
the frequency is switched around the middle frequency , and , as w as ul-
timately completely correctly calculated yesterday, is the radiation’s loss of fre-
quency as a consequence of its reflection off the atom, which results from the mo-
mentum law. Thus far, esteemed Professor, you were entirely right.
However, the reflected radiation can now just be absorbed by an atom that has
the velocity in the –x direction, whereby upon renewed gain in frequency
in the x direction, the radiation loses the frequency: as a conse-
quence of the reversal of the Doppler effect, and the next frequency loses as
a consequence of the momentum conservation law.
The net frequency for both processes is:
ν0
v1ν0
c
---------- v1
Radiation before the process
1. Process
v1
v1 ε
hν0
mc
-------- =
m
2
--- -v1 2
m
2
--- -( v1 ε)2 2mv1ε 2mε2 hΔν = =
Δν
2mv1ε
h
--------------- - 2m----
ε2
h
-–
2ν0v1
c
------------- -
2---------0
hν2
c2m
= =
2ν0v1
c
------------- -
ν0 2---------
hν0
2
c2m
v1
2ν0( v1 2ε)
c
------------------------------ -
2hν02
c2m
------------
2ν0v1
c
------------- -
2hν0 2
c2m
------------
2ν0( v1 2ε)
c
------------------------------ -
2hν0 2
c2m
------------ 0. =
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