Separate HTML for Basic Foil 5 Operations used with Hamiltonian operator

Basic HTML version of Foils prepared 6 December 96

Foil 5 Operations used with Hamiltonian operator

From Full Matrices - December 4, 1995 CPS615 Basic Simulation Track for Computational Science -- Fall Semester 95. by Geoffrey C. Fox, Nancy J. McCracken

Often you want to find eigenstates

where operator H is diagonal with respect to basis set . However, this is usually impossible.

Often one knows that

for example, if the compound is ,then is the "free" Hamiltonian for isolated molecules

and is the interaction, i.e. the forces between atoms.

Simple states diagonalize , but will be nonzero for "most" i and j.