Wikipedia:Reference desk/Archives/Mathematics/2014 June 4

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June 4

Normalising a molecular orbital

How do I find the coefficients of the following wave-function through normalization?

Ψ = c₁φ₁ + c₂φ₂ - c₁φ₃ - c₂φ₃ + c₁φ₄ + c₂φ₅ - c₁φ₆ - c₂φ₆? Plasmic Physics (talk) 23:00, 4 June 2014 (UTC)

What do you know about the $\varphi _{i}$'s?? Are they orthonormal? If they are, you can probably just use that to calculate $\langle \Psi |\Psi \rangle$ and set that to 1. I expect you'll get an equation for your coefficients $c_{i}$ that has some freedom of choice built in, but that is fine (one equation is not enough to determine two unknowns completely). —Kusma (t·c) 11:27, 5 June 2014 (UTC)

No, they're not orthonormal; they are parallel though. The wave function is derived using Hückel method applied to benzene. Plasmic Physics (talk) 12:44, 5 June 2014 (UTC)

Normalization can only eliminate one real degree of freedom: a single overall real scalar multiplier of the coefficients. Beyond that, normalization cannot tell you anything about the coefficients, though an overall phase factor can normally be ignored. I'm not sure what you're hoping to derive by this approach. —Quondum 13:30, 5 June 2014 (UTC)

How else do I then find the coefficients, given the secular equation? Plasmic Physics (talk) 14:14, 5 June 2014 (UTC)