While this seems pretty magical, the biggest challenge will be inverting the Hamiltonian in the first place. As we saw with the variational method, an example can be helpful in demonstrating the technique. Let’s just consider our familiar infinite square well, again setting its width a = 1 for simplicity. That is, the potential is

In the well, the Hamiltonian is of course exclusively kinetic energy:

in  position  space.  To  use  this  power  method  to  find  the  ground  state,  we  need  to determine what the inverse of this Hamiltonian is; that is

or, what is the inverse of the momentum operator 1/pˆ ?

Transcribed Image Text:

V(x) = = {2 0, 0 < x < 1, (10.70) o, x <0, x>1.