Many proteins contain metal porphyrin molecules that can be modeledas a planar square with an edge length of 10A. The π systemcan be described as electrons in a box.

1. Write down the schroedinger equation for the square and find theeigenvalue sand eigenfunctions of the system.

2. Use the electron mass 9*10^-31 kg and h = 10^-34 Js and thelength of the edge of the square to determine the energy levels incm^-1 as a function of the two indicies nx andny for the particle in a square. (it is recommended towork first with a single system in m/kg/s and then convert theresults to cm^-1.

3. Electrons enter the wavefunctions as pairs. Ie to everywavefunction we can put two electrons and we start with the lowestenergy states and go up. The heme has 18 electrons. What is the lowest energy absorption (moving electron from occupied to emptyorbital) that we can have in the mode? ( experimentally theexcitation is of 17,000 cm^-1)