He atom

1. What is the variation theorem and how is it used in quantum mechanical calculations?

2. If we neglect electron-electron repulsion, He has an easy solution. Show what Y is and how the Schrodinger equation is satisfied. What is the energy of the lowest state of He by this model?

3. Write down the Schrodinger equation for the Li⁺² in atomic units.

4. Write down the Schrodinger equation for He and show that Hy is

{2E_H,Z=2 + e²/(4per12)}y

when y = 1s² where 1s is the eigen function for the 1 s H like orbital when Z=2.

5. The electron energy of the He atom is about -2.9 atomic units? What is this energy in J/atom? What is the shielding of the electrons of He?

6. In atomic units what are the following:

a) the Bohr radius

b) the energy of the H atom in the ground state

c) the mass of the electron

d) the energy of the He+ ion in its ground state.

e) the potential energy of the electron in the H atom in its ground state