Write the inner product of the state vector in a atom orbital

1. Jul 28, 2013

rishhary

Consider 2 atomic orbitals with wave function a: σ(r), b: μ(r) in a diatomic molecules. σ(r) (or μ(r)) is localized around an atom a (or b) and is relevant for the discussion of the molecular orbital. These orbitals are orthogonal and normalised. The creation operators are x, y and vacuum, |0>.

a ) A wave function for the orbital on each atom is represented by the creation operator. Using the bra vector <r| write σ(r), μ(r) in the inner product of the state vectors.

b) Let ε^a (or ε^b) be the energy of a: σ(r), b: μ(r) respectively and V = <0|xHy|0> be a real matrix element. Obtain the energy eigen values in this Linear combination of atomic orbitals approach.

These questions are from a sample exam papers of my course and I tried solving them but I am not sure of my answer so I decided to post it here so I can get some feedback and cross-check my solution. Thank you

2. Jul 29, 2013

Staff: Mentor

Please post your solution here (and use the homework template), otherwise you cannot get feedback on it.