Then . Let be parameterized by some set of parameters. This gives a decent bound on ground state energy.

steps:

When you choose to vary by every point, you get:

Integrating by parts, you get: . Demanding this be 0 at every point gives the schrodinger equation.

For non-ground states, may just have stationary states rather than minimum after variation.

source

psfile jl@crush.caltech.edu index

variational_helium