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by “reasonably stable” metastable states, it fulfills the crucial condition
above (Von Foerster, 1964).
Let
sin
2p
x
Ê
Ë
ˆ
¯
V
=±
e
-
xk
+
B
(59)
p
with
A/B
>> 1
and k
/p
>> 1
be the potential distribution in two one-dimensional linear “periodic crys-
tals,” C
+
and C
-
, where the ± refer to corresponding cases. The essential dif-
ference between these two linear structures which can be envisioned as
linear distributions of electric charges changing their sign (almost) periodi-
cally is that energy is required to put “crystal”
C
+
together, while for
“crystal”
C
-
about the same energy is required to decompose it into its
constituents. These linear lattices have metastable equilibria at
C
+
Æ
x
1
,
x
3
,
x
5
...
C
-
Æ
x
0
,
x
2
,
x
4
...
which are solutions of
xk
cos
2
p
x
p
1
2
Ap
B
e
=
ª
1
pk
These states are protected by an energy threshold which lets them stay in
this state on the average of amount an time
t=t
0
e
D
/kT
(60)
where t
0
-1
is an electron orbital frequency, and D
V
is the difference between
the energies at the valley and the crest of the potential wall [±D
V
n
=
V
(
x
n
)
-
V
(
x
n
+1
)].
In order to find the entropy of this configuration,
we solve the
Schrödinger equation (given in normalized form)
[
-
()
]
=
(61)
yyl
Vx
¢¢ +
0
for its eigenvalues l
i
and eigenfunctions y
i
, y
i
*, which, in turn, give the prob-
ability distribution for the molecule being in the
i
th eigenstate:
dp
dx
Ê
Ë
ˆ
¯
=yy
*
(62)
i
i
i
with, of course,
+•
Ú
yy
i
◊
*
dx
=
1
(63)
i
-•
whence we obtain the entropy
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