Physical Problems Solved by the Phase-Integral Method

2002 ◽  
Author(s):  
Nanny Fröman ◽  
Per Olof Fröman
Keyword(s):  
Integral Method ◽  
Physical Problems ◽  
Phase Integral

The Jost function treated by the F-matrix phase integral method

1979 ◽  
Vol 12 (2) ◽  
pp. 171-186 ◽  
Author(s):  
G Drukarev ◽  
N Froman ◽  
P O Froman
Keyword(s):  
Integral Method ◽  
Matrix Phase ◽  
Jost Function ◽  
Phase Integral

Semiclassical model calculations of weak, strong, and short H-bonds

1991 ◽  
Vol 69 (11) ◽  
pp. 1819-1826 ◽  
Author(s):  
Werner A. P. Luck ◽  
Thomas Wess
Keyword(s):  
Integral Method ◽  
Basis Set ◽  
Bond Energies ◽  
Model Calculations ◽  
Semiclassical Model ◽  
Phase Integral ◽  
Simple Phase ◽  
Tunnel Effects ◽  
Isotopic Effects ◽  
Ubbelohde Effect

The OH potentials of the complexes [Formula: see text] are calculated by an ab initio MO-LCAO-SCF-CISD method with a 6-31G** basis set for 30 different [Formula: see text] distances. The resulting OH vibration levels are calculated by the so-called semiclassical Planck–Sommerfeld phase integral. The experimental H-bond effects on vibration spectra, and their anomalies, could be established by calculations of H-bond energies, OH frequencies, anharmonicities, the Badger–Bauer rule, correlation between OH and [Formula: see text] distances, isotopic effects, and the Ubbelohde effect. For very short H-bonds new properties could be predicted. There seem to exist three classes of H-bond: (1) weak or medium-strong, (2) strong, and (3) very short. The simple phase integral method could demonstrate the anomalous effects of strong H-bonds solely by the transition from two separated minima to one, without necessarily assuming tunnel effects. Key words: strong H-bonds, IR spectra and theory, tunnel effects.

Theory of the modulation imposed on an obliquely incident radio wave reflected in a disturbed region of the lower ionosphere

1976 ◽  
Vol 349 (1659) ◽  
pp. 555-570 ◽  
Keyword(s):  
Integral Method ◽  
Collision Frequency ◽  
Lower Ionosphere ◽  
Electron Collision ◽  
Disturbed Region ◽  
Quartic Equation ◽  
Obliquely Incident ◽  
Electron Collision Frequency ◽  
Reflexion Coefficient ◽  
Phase Integral

A powerful disturbing wave enters the lower ionosphere and causes a periodic modulation of the electron collision frequency. A simple model is adopted for this disturbed region. The modulation transferred to an obliquely incident wanted wave that is reflected in or near it is investigated. The reflexion coefficient of the wanted wave is found by applying the phase integral method. The complex reflexion height of the wanted wave is a function of time in the modulation cycle. Results are discussed first for an isotropic ionosphere and are then extended to include the effect of the Earth’s magnetic field, and the calculation uses the Booker quartic equation. It is shown that the phase integral method is admirably suited to solve this kind of problem. Some examples are given to illustrate that the greatest amount of modulation is transferred when the wanted wave is reflected near the most disturbed part of the ionosphere. The relation of this to some observed effects near sunrise is discussed.

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