Problem
set: Organic Molecules, Electronic Structures, Properties and Reactions
ELEG
667–016; MSEG-667-016 - Solid
State Nanoelectronics –
Fall 2004
Homework #4 - Due 12 Oct 2004
- The
wave function for a particle moving between 0 and a in a one-dimensional
box is Y
= (2/a)½ sin(npx/a). Calculate the probability that the
particle be found in the middle third of the box (i.e., between x = a/3
and 2a/3) for n = 1, 2, 3.
- Within
the Hückel approximation, write down the secular determinant for benzene pz
orbitals to yield the molecular p-orbitals
of benzene (C6H6).
- One
reason that we do not see the effects of quantum resistors is because
there are many possible modes. In
Landauer formalism the conductivity for one mode is given by G = (2e2/h)(T/R). What would the conductivity be for M modes, in parallel?