M O M E N T O F M O M E N T U M 5 8 7
Hence:
(5)
and, by (2), if the equation
is taken into account,
. . . (6)
Comparing this with (1), one sees that the magnetic moment is given by
and in the case of a number of electrons, in stationary motion within a small space, and hav-
ing equal charges e, by
(7)
The moment of momentum M being given by
or by
if the electrons have equal masses m, we are led to the relation
V1
1
2
-- - f2
1
r
-
∂--
∂x3
------- - – f3
r
-
∂--1
∂x2
------- - +
e
c
-- =
Δ
1
r
-- -
è ø
æ ö
0 =
hx
e
2c
----- - f1
2
2
∂x1
∂ 1
r
-- -
è ø
æ ö
e
2c
----- - f2
x1∂x2
2
∂
∂ 1
r
-- -
è ø
æ ö
e
2c
----- - f3
x1∂x3
2
∂
∂ 1
r
-- -
è ø
æ ö
+ + =
e
2c
----- - f =
e
2c
----- -
Σ
f =
[p. 3]
M
Σ
mf =
M
mΣ
f =
M
---- -
2mc
e
---------- =