Re: One more question about the "Note on Recursion Methods" ( No.1 ) 
 Date: 2007/10/21 09:56
 Name: T.Ozaki
 Hi,
> I am wondering if there is a mistake in Eq. (2.37) on page 40 of your notes, > should the \hat{H} be \hat{H'} where H'=S^{1}H ?
It is correct as the symbolic notation, since the state in the lefthand side is written by the dual vector. But, your guess is right in practice since the original basis is used to represent the Hamiltonian.
> To compute the r_n) in Eq.(2.37), we need first explicitly > compute H' by using H'=S^{1}*H, right?
Instead, the following second step calculation can reduce the computational time. (i) (V = (UnS^{1} (ii) (VH But, as the recursion level is comparable to the matrix size of original Hamiltonian, they become comparable each other with respect to computational time.
Regards,
TO

