Resonances in the Continuum, Field-Induced Nonstationary States, and the State- and Property-Specific Treatment of the Many-Electron Problem

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Resonances in the Continuum, Field-Induced Nonstationary States, and the State- and Property-Specific Treatment of the Many-Electron Problem

Νικολαΐδης, Κλεάνθης A.

Κεφάλαιο βιβλίου

2017


The paper summarizes elements of theories and computational methods that we have constructed and applied over the years for the nonperturbative solution of many-electron problems (MEPs), in the absence or presence of strong external fields, concerning resonance/nonstationary states with a variety of electronic structures. Using brief arguments and comments, I explain how these MEPs are solvable in terms of practical time-independent or time-dependent methods, which are based on single- or multistate Hermitian or non-Hermitian formulations. The latter result from the complex eigenvalue Schrödinger equation (CESE) theory. The CESE has been derived, for field free as well as for field-induced resonances, by starting from Fano's 1961 discrete-continuum standing-wave superposition, and by imposing outgoing-wave boundary conditions on the resulting solution. Regularization is effected via the use of complex coordinates for the orbitals of the outgoing electron(s) in each channel. The Hamiltonian coordinates remain real. The computational framework emphasizes the use of appropriate forms of the trial wavefunctions and the choice of function spaces according to the state- and property-specific methodology, using either nonrelativistic or relativistic Hamiltonians. In most cases, the bound part of excited wavefunctions is obtained via state-specific “HF or MCHF plus selected parts of electron correlation” schemes. This approach was first introduced to the theory of multiply excited and inner-hole autoionizing states in 1972, and its feasibility was demonstrated even in cases of multiply excited negative-ion scattering resonances. For problems of states interacting with strong and/or ultrashort pulses, the many-electron time-dependent Schrödinger equation is solved via the state-specific expansion approach. Applications have produced a plethora of numerical data that either compare favorably with measurements or constitute testable predictions of properties of N-electron field-free and field-induced nonstationary states.

Φυσική και θεωρητική χημεία (EL)
Ατομική φυσική (συμπ. μοριακή φυσική, σχετικότητα, κβαντική θεωρία και φυσική στερεάς κατάστασης) (EL)
Atomic physics (Incl. molecular physics, relativity, quantum theory, and solid state physics) (EN)
Physical and theoretical chemistry (EN)

Many-electron problems (EN)
Resonances (EN)
Strong fields (EN)
Complex eigenvalue Schrödinger equation (EN)
Time-dependent Schrödinger equation (EN)
Field-induced nonstationary states (EN)

Αγγλική γλώσσα

Academic Press Inc.


Advances in Quantum Chemistry

© 2017 Elsevier Inc.
© 2017 Elsevier Inc. (EN)




*Η εύρυθμη και αδιάλειπτη λειτουργία των διαδικτυακών διευθύνσεων των συλλογών (ψηφιακό αρχείο, καρτέλα τεκμηρίου στο αποθετήριο) είναι αποκλειστική ευθύνη των αντίστοιχων Φορέων περιεχομένου.