4 problems

Exchange-energy conjecture. The exchange energy should be given by a term of the form

Let $I_\Psi$ be the exchange energy … where $\Psi$ is an appropriate atomic wave function in the lowest Landau band, $D$ is the Coulomb self-energy pairing, and $\rho_\Psi$ is the…

Linear-molecule conjecture. The presence of a strong magnetic field can lead to the formation of linear molecules (linear chains) situated along magnetic lines.

Let $Z$ be the nuclear charge and $B$ the magnetic-field strength. Consider the actual molecule modelled by the Pauli Hamiltonian, and let its equilibrium distance be denoted by…