Chemistry Reference
In-Depth Information
15. Equate the bondonic chemical bond field with the chemical field quanta (10.3)
to get the bondons' mass
ℵ
B
(m
B
)
=ℵ
0
.
(10.8)
This algorithm will be next unfolded both for non-relativistic as well as for relativistic
electronic motion to quest upon the bondonic existence, eventually emphasizing their
difference in bondons' manifestations.
In treating the quantum relativistic electronic behavior, the consecrated starting
point stays the Dirac equation for the scalar real valued potential w that can be seen
as a general function of (
tc
,
x
) dependency (Dirac
1928
)
+
βw
↔
0
k
=
1
α
k
∂
k
+
βmc
2
3
h∂
t
↔
0
=
i
−
i
hc
(10.9)
¯
¯
with the spatial coordinate derivative notation
∂
k
≡
∂/∂x
k
and the special operators
assuming the Dirac 4D representation
⎡
⎤
⎡
⎣
ˆ
10
0
⎤
ˆ
0
σ
k
⎣
⎦
,
β
⎦
α
k
=
ˆ
=
(10.10a)
−
ˆ
1
σ
k
0
ˆ
in terms of bi-dimensional Pauli and unitary matrices
⎡
⎤
⎡
⎤
⎡
⎤
⎡
⎤
01
10
0
−
i
i
0
10
0
10
01
⎣
⎦
,
⎣
⎦
,
⎣
⎦
,
ˆ
1
⎣
⎦
σ
1
=
ˆ
σ
2
=
ˆ
σ
3
=
ˆ
≡ˆ
σ
0
=
(10.10b)
−
1
Written within the de Broglie-Bohm framework, with the
R
-amplitude and
S
-phase
action factors given, respectively, as
0
(
t
,
x
)
2
ρ
1
/
2
(
x
)
R
(
t
,
x
)
=
=
(10.11a)
S
(
t
,
x
)
=
px
−
Et
(10.11b)
in terms of electronic density
ρ
, momentum
p
, total energy
E
, and time-space (
t
,
x
)
coordinates the spinor solution of Eq. (10.9) looks like
⎡
⎣
⎤
⎦
ϕ
1
√
2
R(t
,
x)
↔
0
=
φ
exp
i
¯
s
]
⎡
⎤
1
2
,
s
=±
h
[
S
(
t
,
x
)
+
⎣
⎦
1
√
2
=
R(t
,
x)
exp
s
]
(10.12a)
i
¯
−
h
[
S(t
,
x)
+
