Have hamiltonian H, pick wave function tex2html_wrap110

Then tex2html_wrap111 . Let tex2html_wrap112 be parameterized by some set of parameters. This gives a decent bound on ground state energy.

steps:

  1. tex2html_wrap113
  2. tex2html_wrap114

When you choose to vary tex2html_wrap115 by every point, you get:

tex2html_wrap116

tex2html_wrap117

Integrating by parts, you get: tex2html_wrap118 . 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