The adiabatic theorem in the complex plane and the semiclassical calculation of nonadiabatic transition amplitudes

摘要: This paper is concerned with the problem of calculating amplitudes for nonadiabatic transitions induced by a time‐dependent Hamiltonian, in semiclassical limit h/→0, emphasis on questions relevant to theories electronically inelastic scattering. For this mathematically equivalent adiabatic limit, and theorem says that all these transition vanish limit; question is, what asymptotic form amplitudes, as they go zero? We consider Hamiltonia are analytic matrix functions time. prove generalization complex time plane; paradoxically, plane gives us directly along real axis. derive Dykhne’s remarkable formula two‐state case, which limiting amplitude depends only energy curves two states, not nonad...