1a. Write down the Schrodinger equation for H₂⁺.

1b. Show that when a linear combination of atomic orbitals is used for the molecular orbital that

Hy = c₁E_Hy₁ + c₂E_Hy₂ + 1/R(y) + c₁y₁(1/r₂) + c₂y₂(1/r₁)

2. Write down the Schrodinger equation for H₂. Use 1 and 2 as subscripts to indicate the electron and A and B to indicate the protons so that r1A would indicate the distance from electron 1 to nucleus A, etc.

3. Write equation 11.5 in atomic units.

4. What will be the value of y =c₁y₁ + c₂y₂ for H₂⁺ at r=1.5 from H1 and on the bonding axis when R= 2 atomic units. Use equal coefficients of 0.707.