Information Technology Reference
In-Depth Information
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
Search WWH ::




Custom Search