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rishhary
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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
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