### Abstract

A rigorous and practical time-dependent formulation of quantum decay processes is obtained by converting the Hermitian Schrodinger problem into an equivalent non-Hermitian Schrodinger equation. The properties of the original Hermitian and the reduced non-Hermitian Hamiltonians are compared and the non-Hermitian formulation is shown to be consistent with the theorem of Fock and Krylov for the description of truly decaying states. A self-consistent non-unitary algorithm is developed and used to obtain expressions for the time-dependent transition amplitudes of interest; they automatically preserve the total probability in the sum space at all future times tau >0. The formalism is coded for application to the important problem of ionisation decay of a ground-state hydrogen atom coupled to a strong radiation field with a sub-threshold photon frequency. The first quantitative information on the time dependence of two- and three-photon (resonant and non-resonant) ionisation of the hydrogen atom is obtained.

Original language | English (US) |
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Article number | 012 |

Pages (from-to) | 3603-3620 |

Number of pages | 18 |

Journal | Journal of Physics B: Atomic and Molecular Physics |

Volume | 14 |

Issue number | 19 |

DOIs | |

State | Published - Dec 1 1981 |

Externally published | Yes |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics