Chemistry Reference
In-Depth Information
∂R
∂t
+
h
R
∂S
exp
i
¯
S
∂
U
(1)
∂t
i
¯
e
c
∂
∂t
e
c
ℵ
=
∂t
+
+
(11.11c)
h
leading with the decomposition of the corresponding Schrödinger U(1) equation on
the imaginary and real parts respectively:
∂R
∂x
∂R
∂x
∂
2
S
∂x
2
∂
2
∂R
∂t
=
1
m
∂S
∂x
+
R
2
e
mc
∂
∂x
+
R
2
ℵ
∂x
2
−
+
(11.12a)
∂S
∂x
2
2
e
c
h
2
2
m
∂
2
R
∂x
2
R
∂S
R
e
c
∂
∂t
=−
¯
R
2
m
∂
∂x
−
∂t
−
+
+
(11.12b)
mc
R
∂S
e
∂
∂x
+
+
VR
∂x
that can be further rearranged as:
R
2
∂S
∂x
R
2
∂
∂R
2
∂t
=
∂x
1
m
∂
∂x
e
mc
∂
∂x
−
+
(11.13a)
∂S
∂x
2
∂S
∂t
+
2
e
c
h
2
2
m
∂
2
R
∂x
2
e
c
∂
∂t
1
R
1
2
m
∂
∂x
=−
¯
−
+
+
(11.13b)
e
mc
∂S
∂x
∂
∂x
+
+
V
Equations (11.13) reveal some interesting features of the chemical bonding to be in
next discussed.
The Eq. (
11.13a
) provides the conserving charge current with the form:
−
∇
S
+
R
2
m
e
c
−
∇ℵ
j
U(1)
=
=
j
S
+
j
(11.14)
ℵ
leaving with idea that additional current is responsible for the chemical field to be
activated, namely:
e
mc
R
2
−
∇ℵ
ℵ
=
j
(11.15)
which vanishes when the
global gauge
condition is considered, i.e. when
∂
∂x
=
0
(11.16)
Therefore, in order the chemical bonding be created the
local gauge
transformation
should be used that is
∂
∂x
=
0
(11.17)
