Schrodinger equation lower bound method

By replacing the wavefunction with a density matrix, the electronic structure problem is reduced in size to that for a two- or three-electron system. Rather than solve the Schrodinger equation to determine the wavefunction, the lower bound method is invoked to determine the density matrix this requires adjusting parameters so that the energy content of the density matrix is minimized. More precisely, the lower bound method requires finding a solution to the energy problem,... 

We have focused on the lower bound method, but density matrix research has moved forward on a much broader front than that. In particular, work on the contracted Schrodinger equation played an important role in developments. A more complete picture can be found in Coleman and Yukalov s book [23]. It has taken 55 years and work by many scientists to fulfill Coleman s 1951 claim at Chalk River that except for a few details which would be easily overcome in a couple of weeks—the A-body problem has been reduced to a 2.5-body problem ... 

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