Biomedical Engineering Reference
In-Depth Information
I have emphasized earlier the interplay between spectroscopic data and theoretical
developments; even before Schrödinger's time many highly precise spectroscopic data
had been obtained experimentally. The traditional reference sources for such data are the
three volumes of tables in the
Atomic Energy Levels
series (Moore 1949, 1952, 1958).
In the past few years, the National Institute of Standards and Technology (NIST) atomic
spectroscopists have made available a unified comprehensive Atomic Spectra Database
on the World Wide Web, which contains spectral reference data for 91 000 wavelengths
(http://www.nist.gov). The sample in Table 13.5 is taken from the database. Note that the
data contains
spectroscopic term symbols
for each level, which are discussed in all ele-
mentary physical chemistry undergraduate texts. Spectroscopists traditionally deal with
term values
rather than energies; these are just ε/
hc
0
.
Table 13.5
Internet search for atomic term values
Configuration
Term symbol
j
Term value/cm
−1
1s
1
2
S
1/2
0
2p
1
2
P
1/2
82 258.9206
3/2
82 259.2865
2s
1
2
S
1/2
82 258.9559
3p
1
2
P
1/2
97 492.2130
3/2
97 492.3214
3s
1
2
S
1/2
97 492.2235
3d
1
2
D
3/2
97 492.3212
5/2
97 492.3574
4p
1
2
P
1/2
102 823.8505
3/2
102 823.8962
4s
1
2
S
1/2
102 823.8549
4d
1
2
D
3/2
102 823.8961
5/2
102 823.9114
4f
1
2
F
5/2
102 823.9113
7/2
102 823.9190
13.11 Dirac Theory of the Electron
There is no mention of electron spin from the Schrödinger equation, and certainly no clue
as to why the classical equation for magnetic moments is in error by (roughly) a factor
of 2 when applied to electron spin (Equation (13.36)). If we consider the time-dependent
Schrödinger equation for a free electron
∂
2
∂
x
2
+
Ψ (
r
,
t
)
h
2
8π
2
m
e
∂
2
∂
y
2
+
∂
2
∂
z
2
j
h
2π
∂
∂
t
Ψ (
r
,
t
)
−
=
(13.37)
(where j is the square root of
1), it is seen to be a second-order partial differential equation
with respect to the spatial coordinates and a first-order partial differential equation with
respect to time. It therefore is not consistent with the special theory of relativity, which
requires that time and space should enter such equations on an equal footing. If the equation
is second order in space, it should also be second order in time.
−
