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Fröman N., Fröman P.O. — JWKB approximation: contributions to the theory
Fröman N., Fröman P.O. — JWKB approximation: contributions to the theory

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Название: JWKB approximation: contributions to the theory

Авторы: Fröman N., Fröman P.O.

Аннотация:

The book contains a rigorous treatment of the one-dimensional JWBK-approximation. Using the ideas introduced by Zwaan and Kemble as a starting point we develop a method for examining the properties of the JWKB-approximation which is powerful also in intricate and complicated applications. In the first place we have had quantal problems in mind and hence, in the main part of the book, we assume the coefficients of the differential equation considered to be real on the real axis. This assumption simplifies the treatment. There are, however, important applications, for instance in the theory of electromagnetic waves, where the reality condition is not fulfilled. It should therefore be pointed out that the general theory in chapters 3, 4, and 7, is not subject to the above mentioned restriction and that the method can be worked out also when the coefficients are complex.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1965

Количество страниц: 138

Добавлена в каталог: 06.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
a-coefficients      see also “a-vector”
a-coefficients, definition of      15
a-coefficients, differential equations for      15
a-coefficients, limiting properties of      29 92 103—105 115—116
a-vector      see also “a-coefflcients”
a-vector, definition of      16
a-vector, differential equation for      16
a-vector, integral equation for      16
Anti-Stokes' line      60
Asymptotic approximation method      1
Asymptotic phase      125—130
Asymptotic phase, exact expressions for      126 128
Basic Estimates      26—27
Bethe      132
Birkhoff      3 4
Bohm      7 97
Brillouin      1
Carlini      1
Classical turning point      34
Classical turning point, in the generalized sense      34 80
Classically allowed region      34
Classically allowed region, in the generalized sense      34 80
Classically forbidden region      34
Classically forbidden region, in the generalized sense      34 80
Connection formulae      1—3 6—8 83—89 97
Connection formulae, derivation of      83—86
Connection formulae, one-directional (one-sided) nature of      2 6—8 40 46 86—89 97
Current density      7 91
Epsilon, $\varepsilon,$ definition of      13
Estimates of the F-matrix      chapters 4 6 7
F-functions, definition of      20
F-matrix, basic estimates of      26—27
F-matrix, definition of      16
F-matrix, determinant of      17—18
F-matrix, differential equation for      17
F-matrix, estimates of      see “Estimates of the F-matrix”
F-matrix, integral equation for      17
F-matrix, inversion of      18
F-matrix, limiting properties of      27—29 92 103
F-matrix, multiplication rule for      21
F-matrix, series for      16 18—20
F-matrix, symmetry properties of      30—33
F-vector, definition of      20
Feshbach      7
GANs      1
Generalized classical turning point      34 80
good      94
Green      1
Harmonic oscillator, linear      109
Harmonic oscillator, three-dimensional      120—125
Heading      1 3 4 7 88 97
Hecht      14
Hydrogen-like ion      117—120 131—132
Jeffreys, B.S.      1 94
Jeffreys, H.      1 2 7 88 97
JWKB-approximation      1—2
JWKB-approximation, first order      11
JWKB-approximation, modified      4 110
JWKB-approximation, second order      10
JWKB-method      see “JWKB-approximation”
Kemble      3—5 8 15 86 90 91 94 112
Kramers      1 112
Langer      2 6 86 88 97 112 113 130 131 133 134
Liouville      1
Liouville — Green approximation      1
Loewdin      14
Mayer      14
Merzbacher      7 51 97
Messiah      86
Miller      94
Morse      7
Mu-integral, $\mu$-integral, definition of      26
O-symbol      2—3 45—46
Olver      3 23—25 27 35
Pauli      7
Phase-integral method      1
Potential barrier, overdense      34 43—51
Potential barrier, parabolic      51 59 91 94 99
Potential barrier, underdense      34 51—59
Potential well      102
Probability current      91
Quantization condition      105—109 115—116
Quantization condition, exact      106 108 116
Quantization condition, semi-classical      4 9 108—109 116 117 119 121—125
Reflection coefficient, approximate expressions for      94 101
Reflection coefficient, exact expressions for      93 99—100
Salpeter      132
Schiff      86
Schwarzian derivative      14
Seifert      2
Semi-classical quantization condition      see “Quantization condition”
Stokes' constants      4
Stokes' line      60
Stokes' phenomenon      5 6 12 23 74
Symmetry relations      5 30—33
Transition point      34
Transmission coefficient, approximate expressions for      90—91 94 101
Transmission coefficient, exact expressions for      93 99—100
Turning point      see “Classical turning point”
w(z), definition of      13
Wave function, exact expression for      20
Wentzel      1
WKB-method      1
Zwaan      3
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