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

1. 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.

2. Within the Hückel approximation, write down the secular determinant for benzene p_z orbitals to yield the molecular p-orbitals of benzene (C₆H₆).

3. 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?