@@ -394,7 +394,7 @@ Which term needs to be added to the Hamiltonian of each electron?
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@@ -394,7 +394,7 @@ Which term needs to be added to the Hamiltonian of each electron?
Compute the LCAO Hamiltonian of the system in presence of the electric field.
Compute the LCAO Hamiltonian of the system in presence of the electric field.
What are the new onsite energies of the two orbitals?
What are the new onsite energies of the two orbitals?
#### Question 3.
#### Question 3.
Diagonalize the modified LCAO Hamiltonian. Find the ground state wavefunction $ψ$.
Diagonalize the modified LCAO Hamiltonian. Find the ground state wavefunction $ψ$. Note: for simplicity assume that the electric field is small, such that $\gamma \ll t$, with $\gamma = e d \mathcal{E}/2$.
#### Question 4.
#### Question 4.
Find the polarization $P$ of the molecule in the ground state.
Find the polarization $P$ of the molecule in the ground state.