Effective Hamiltonian mappings

R. W. Field Prof. Rabitz, I like the idea of sending out a scout to map a local region of the potential-energy surface. But I get the impression that the inversion scheme you are proposing would make no use of what is known from frequency-domain spectroscopy or even from nonstandard dynamical models based on multiresonance effective Hamiltonian models. Your inversion scheme may be mathematically rigorous, unbiased, and carefully filtered against a too detailed model of the local potential, but I think it is naive to think that a play-and-leam scheme could assemble a sufficient quantity of information to usefully control the dynamics of even a small polyatomic molecule. 

Effective Operators and Classification of Mapping Operators Effective Operators Generated by Norm-Preserving Mappings Effective Operators Generated by Non-Norm-Preserving Mappings which Produce a Non-Hermitian Effective Hamiltonian... 

Appendix B Non-Norm Preserving Mappings that Produce a Hermitian Effective Hamiltonian Appendix C Proof of Theorem I... 

Consider a time-independent operator A whose matrix elements, yf a, /3 d (both expectation values and transition moments), in the space fl we wish to compute. This goal is to be achieved by transforming the calculation from 0 into one in O, resulting in an effective operator a whose matrix elements, taken between appropriate model eigenfunctions of an effective Hamiltonian h, are the desired As we now discuss, numerous possible definitions of a arise depending on the type of mapping operators that are used to produce h and on the choice of model eigenfunctions. 

Norm-preserving mappings these necessarily generate a Hermitian effective Hamiltonian ... 

Norm-preserving mappings are denoted by K, fC) and, as discussed in Section II.B, generate a Hermitian effective Hamiltonian K HK = i. The orthonormalized model eigenfunctions of H are written as a)o and the corresponding true eigenfunctions are designated by I Pa). Thus, Eq. (2.2) specializes to... 

Mappings Norms Conserved" Effective Hamiltonian Effective operator definition Effective Hamiltonian is the A = H Case State- Independent... 

Mappings which Produce a Hermitian Effective Hamiltonian... 

Fock Space Diagonal Definition Variant W Unitary Effective Hamiltonian h Hermitian Corresponding Mapping Category... 

Section II.D shows how the mappings K, L) generate the non-Hermitian effective Hamiltonian H = LHK corresponding to H,... 

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