Physical Problems Solved by the Phase-Integral Method

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

Journal of Physics A General Physics ◽

10.1088/0305-4470/12/2/004 ◽

1979 ◽

Vol 12 (2) ◽

pp. 171-186 ◽

Cited By ~ 24

Author(s):

G Drukarev ◽

N Froman ◽

P O Froman

Keyword(s):

Integral Method ◽

Matrix Phase ◽

Jost Function ◽

Phase Integral

Regge-pole description of rainbow scattering by means of the phase-integral method

Physical Review A ◽

10.1103/physreva.50.1420 ◽

1994 ◽

Vol 50 (2) ◽

pp. 1420-1428 ◽

Cited By ~ 10

Author(s):

Abraham Amaha ◽

Karl-Erik Thylwe

Keyword(s):

Integral Method ◽

Regge Pole ◽

Phase Integral ◽

Rainbow Scattering

Calculation of expectation values and matrix elements for symmetric double-well potentials. I. General theory according to phase-integral method

Annals of Physics ◽

10.1016/0003-4916(85)90379-3 ◽

1985 ◽

Vol 163 (2) ◽

pp. 227-244 ◽

Cited By ~ 10

Author(s):

Rolf Paulsson ◽

Nanny Fröman

Keyword(s):

General Theory ◽

Integral Method ◽

Matrix Elements ◽

Expectation Values ◽

Phase Integral

On the phase-integral method for the radial Dirac equation

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8113/42/39/395203 ◽

2009 ◽

Vol 42 (39) ◽

pp. 395203 ◽

Cited By ~ 2

Author(s):

Giampiero Esposito ◽

Pietro Santorelli

Keyword(s):

Dirac Equation ◽

Integral Method ◽

Phase Integral ◽

Radial Dirac Equation

Computation of inflationary cosmological perturbations in the power-law inflationary model using the phase-integral method

Physical Review D ◽

10.1103/physrevd.75.063518 ◽

2007 ◽

Vol 75 (6) ◽

Cited By ~ 6

Author(s):

Clara Rojas ◽

Víctor M. Villalba

Keyword(s):

Power Law ◽

Integral Method ◽

Inflationary Model ◽

Cosmological Perturbations ◽

Phase Integral

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

Canadian Journal of Chemistry ◽

10.1139/v91-266 ◽

1991 ◽

Vol 69 (11) ◽

pp. 1819-1826 ◽

Cited By ~ 18

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.

Ionospheric equivalent heights of reflection calculated by a full wave method and by the phase integral method

Journal of Atmospheric and Terrestrial Physics ◽

10.1016/0021-9169(62)90083-1 ◽

1962 ◽

Vol 24 (7) ◽

pp. 609-618 ◽

Cited By ~ 12

Author(s):

K.G. Budden ◽

Elisabeth Cooper

Keyword(s):

Integral Method ◽

Wave Method ◽

Full Wave ◽

Phase Integral

The phase-integral method in a problem of singular perturbation theory

Izvestiya Mathematics ◽

10.1070/im8542 ◽

2017 ◽

Vol 81 (2) ◽

pp. 359-390 ◽

Cited By ~ 2

Author(s):

S A Stepin ◽

V V Fufaev

Keyword(s):

Perturbation Theory ◽

Singular Perturbation ◽

Integral Method ◽

Singular Perturbation Theory ◽

Phase Integral

Inverted potential by the phase-integral method: He-Na elastic scattering

Physical Review A ◽

10.1103/physreva.66.052717 ◽

2002 ◽

Vol 66 (5) ◽

Cited By ~ 1

Author(s):

A. Zerarka ◽

Y. Boumedjane ◽

J. Hans

Keyword(s):

Elastic Scattering ◽

Integral Method ◽

Phase Integral

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

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1976.0089 ◽

1976 ◽

Vol 349 (1659) ◽

pp. 555-570 ◽

Cited By ~ 3

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.