How Do Basis Vectors Represent Orbitals in Quantum Chemistry?

[Niles]

Homework Statement

Hi all.

This post is about quantum chemistry, but my question arises when looking at the problem from a physical point of view.

The Schrödinger equation gives us the stationary states of a system, and let's say that we are looking at a system with two stationary states (Dirac notation - but the LaTeX does not work, so bear with me) |1> and |2> with an associated eigenenergy. These two orthonormal states span the Hilbert space we are working in.Now here's my question: I am looking at a figure of a molecule with six orbitals, and now each orbital is represented by an orthonormal basis |1>, |2>, |3>, |4>, ..., |6>. An eigenstate is then a linear combination of these basis-vectors (orbitals) with an associated energy.

Question: How am I do interpret these basis-vectors |1>, |2>, |3>, |4>, ..., |6>? They surely cannot represent stationary states (i.e. solutions to the time-independent Schrödinger equation), because then a linear combination of them would not have an eigenenergy.

Thanks in advance. Any help will be greatly appreciated, since I cannot get help from anywhere else at the moment.Niles.

 

[Niles]

Can I get a moderator to move this thread to the "Advanced Physics Homework Help"? I think it belongs there more than in this section.

Thanks in advance.