[seanifred]

I have this HW question that I've been stumped on for a while (~1/2 hour)...and its only problem number 2 

any help is greatly appreciated

Consider a planar molecule with 18 electrons and approximate its energy levels with
those of a free particle in a two-dimensional, square box of side a . What are the energy
levels of such a molecule and their degeneracies? Consider a = 1000 pm: what is the
predicted lowest energy absorption of the molecule? Would the lowest absorption
increase or decrease for a bigger planar molecule? Explain why.

i will continue working on it and check back periodically for any insights

thanks

[seanifred]

well im going to my professor's office hours tomorrow, and if/when i have an answer, i'll put it up here too in case other people have something similar to work out

but help is still always welcome

[Yggdrasil]

To solve the Schrodinger's equation for your system, try the separation of variables technique (look for an answer of the form Ψ = A(x)B(y), where A is a function that depends only on x and B is a function that depends only on y.  From this, you should be able to reduce the problem to two 1D particle in a box problems.

[seanifred]

the equations we were taught are

Ψ=A(cos(kx))+(sin(kx))
and
Ψ²=(2/a)(sin²((n(pi)x)/a))

i assume im supposed to use the second one?

and where do the 18 electrons come in?

[Yggdrasil]

In order to solve this problem, you are going to need to derive a new equation for the wavefunction of a particle in a 2-dimensional box.  This wavefunction will be similar to the wavefunction of the particle in a 1D box (the equations that you posted), but it will involve both x and y as variables. 

Perhaps it would be useful to start by writing out the Hamiltonian for the system.