- A Helium atom has two electrons bound to aZ= 2 nucleus. We have to add the coulomb
repulsion term (between the two electrons) to the zeroth order Hamiltonian.
H=
p^21
2 m
−
Ze^2
r 1
+
p^22
2 m
−
Ze^2
r 2
+
e^2
|~r 1 −~r 2 |
=H 1 +H 2 +V
The first excited state of Helium has one electron in the 1S state andthe other in the 2S state.
Calculate the energy of this state to zeroth order in the perturbation V. Give the answer in eV.
The spins of the two electrons can be added to give states of totalspinS~. The possible total
spin states ares= 0 ands= 1. Write out the full first excited Helium state which hass= 1
andms=−1. Include the spatial wave function and don’t forget the Pauli principle. Use
bra-ket notation to calculate the energy shift to this state in firstorder perturbation theory.
Don’t do any integrals.
