- #1

- 533

- 1

[tex]

\hat H_e = -\sum_{i = 1}^M \frac{\hbar^2}{2m_e} \Delta_{r_i} + V_{ee} + V_{eN} + V_{NN}

[/tex]

is self-adjoint and therefore has a basis of eigenvalues. (The three V's above are the coulombic nuclear-nuclear, nuclear-electron, and electron-electron interactions.) That [itex]\hat H_e[/itex] is self-adjoint is pretty obvious...but how do we know it's compact?