# A Computational Physics

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1. Feb 11, 2017

### sams

Dear Everyone,

1. Could anyone please explain what is meant by trivial and non-trivial solutions?

2. LCAO:
Ψ = ∑crΦr
Ψ: Molecular orbitals
c: coefficients
Φ: Atomic orbitals
When we talk about basis sets, do we mean here the coefficients or the atomic functions?

Thanks a lot...

2. Feb 11, 2017

### blue_leaf77

http://www.mathwords.com/t/trivial.htm
As far as my experience is concerned, trivial solution is the zero function or vector.
That depends on which you are talking about, molecule or atom. If the former, then the molecular orbitals are the basis if the latter it's the atomic orbital.

3. Feb 11, 2017

### ExplosivePete

When we solve for solutions to differential equations, in physics we are often only interested in nontrivial solutions. I'm not certain of this, but it is my intuition that the space containing the solutions contain some form of a zero element. Physically, we are uninterested in these trivial solutions. So we disregard them.