What are the molecular orbitals of the hypothetical linear H₃⁺ molecule? What would be the wave function of the lowest energy molecular orbital of a hypothetical linear H3+ molecule? 
According to the LCAO method, I feel the lowest energy MO will be 1s(A) + 1s(B) + 1s(C).
Where 1s(A) is the wave function of the 1s orbital of one of the Hydrogen atoms.
This has 0 nodes and has the lowest energy.

Isn't this correst?
The lowest energy MO is : $\psi_1 = (1/2)(\phi_A+ \sqrt2\phi_B+\phi_C)$.

Then comes the MO: $\psi_2 = (1/\sqrt2)(\phi_A- \phi_C)$.

The highest energy MO is  $\psi_3 = (1/2)(-\phi_A+ \sqrt2\phi_B-\phi_C)$.

Where  $\phi$ denotes the atomic orbital $1s$ on each hydrogen atom. $A$, $B$ and  $C$ denote hydrogen atoms, where  $B$ is the central one.