The operator for the square of the angular momentum for an electron in a hydrogenic atom is given below. L̂2 = -ℏ2 [ ∂2/∂θ2 + cot θ ∂/∂θ + (1/sin2 θ) ∂2/∂ϕ2 ] A correct form of the angular function for the px orbital is:

The energies E± (in atomic units) of bonding (+) and antibonding (-) MOs of H2+, obtained by linear combination of 1s orbitals of H-atoms using the variation principle, are [where J is Coulomb integral, K is exchange integral, S is overlap integral]:

Given the trial wavefunction φ(x) = ae-αx2 + be-β|x| for a system with harmonic oscillator potential V(x) = 12mω2x2, the variationally optimized ground-state energy is obtained with the parameters: