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 One more question about the "Note on Recursion Methods" Date: 2007/10/07 15:43 Name: Yang Xu   Dear Prof. Ozaki,Thank you very much. I really appreciate your answer.I just have one more question. It is really important for us.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 ?To compute the |r_n) in Eq.(2.37), we need first explicitly compute H' by using H'=S^{-1}*H, right?Your timely reply will be highly appreciated!!Best regards,Yang Xu
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 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 left-hand 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| = (Un|S^{-1}(ii) (V|HBut, 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

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