# Physical Problems Solved by the Phase-Integral Method. (Record no. 76384)

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000 -LEADER | |
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fixed length control field | 09708nam a22004933i 4500 |

001 - CONTROL NUMBER | |

control field | EBC202083 |

003 - CONTROL NUMBER IDENTIFIER | |

control field | MiAaPQ |

005 - DATE AND TIME OF LATEST TRANSACTION | |

control field | 20191126103136.0 |

006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |

fixed length control field | m o d | |

007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |

fixed length control field | cr cnu|||||||| |

008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |

fixed length control field | 191125s2002 xx o ||||0 eng d |

020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |

International Standard Book Number | 9780511157714 |

Qualifying information | (electronic bk.) |

020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |

Canceled/invalid ISBN | 9780521812092 |

035 ## - SYSTEM CONTROL NUMBER | |

System control number | (MiAaPQ)EBC202083 |

035 ## - SYSTEM CONTROL NUMBER | |

System control number | (Au-PeEL)EBL202083 |

035 ## - SYSTEM CONTROL NUMBER | |

System control number | (CaPaEBR)ebr10021407 |

035 ## - SYSTEM CONTROL NUMBER | |

System control number | (CaONFJC)MIL43394 |

035 ## - SYSTEM CONTROL NUMBER | |

System control number | (OCoLC)437431989 |

040 ## - CATALOGING SOURCE | |

Original cataloging agency | MiAaPQ |

Language of cataloging | eng |

Description conventions | rda |

-- | pn |

Transcribing agency | MiAaPQ |

Modifying agency | MiAaPQ |

050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |

Classification number | QC20.7.W53 F77 2002 |

082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |

Classification number | 530.124 |

100 1# - MAIN ENTRY--PERSONAL NAME | |

Personal name | Fröman, Nanny. |

9 (RLIN) | 52516 |

245 10 - TITLE STATEMENT | |

Title | Physical Problems Solved by the Phase-Integral Method. |

264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |

Place of production, publication, distribution, manufacture | Cambridge : |

Name of producer, publisher, distributor, manufacturer | Cambridge University Press, |

Date of production, publication, distribution, manufacture, or copyright notice | 2002. |

264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |

Date of production, publication, distribution, manufacture, or copyright notice | ©2002. |

300 ## - PHYSICAL DESCRIPTION | |

Extent | 1 online resource (230 pages) |

336 ## - CONTENT TYPE | |

Content type term | text |

Content type code | txt |

Source | rdacontent |

337 ## - MEDIA TYPE | |

Media type term | computer |

Media type code | c |

Source | rdamedia |

338 ## - CARRIER TYPE | |

Carrier type term | online resource |

Carrier type code | cr |

Source | rdacarrier |

505 0# - FORMATTED CONTENTS NOTE | |

Formatted contents note | Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- 1 Historical survey -- 1.1 Development from 1817 to 1926 -- 1.1.1 Carlini's pioneering work -- 1.1.2 The work by Liouville and Green -- 1.1.3 Jacobi's contribution towards making Carlini's work known -- 1.1.4 Scheibner's alternative to Carlini's treatment of planetary motion -- 1.1.5 Publications 1895-1912 -- 1.1.6 First traces of a connection formula -- 1.1.7 Publications 1915-1921 -- 1.1.8 Both connection formulas are derived in explicit form -- 1.1.9 The method is rediscovered in quantum mechanics -- 1.2 Development after 1926 -- 2 Description of the phase-integral method -- 2.1 Form of the wave function and the q-equation -- 2.2 Phase-integral approximation generated from an unspecified base function -- 2.3 F-matrix method -- 2.3.1 Exact solution expressed in terms of the F-matrix -- 2.3.2 General relations satisfied by the F-matrix -- 2.3.3 F-matrix corresponding to the encircling of a simple zero of… -- 2.3.4 Basic estimates -- 2.3.5 Stokes and anti-Stokes lines -- 2.3.6 Symbols facilitating the tracing of a wave function in the complex z-plane -- 2.3.7 Removal of a boundary condition from the real z-axis to an anti-Stokes line -- 2.3.8 Dependence of the F-matrix on the lower limit of integration in the phase integral -- 2.4 F-matrix connecting points on opposite sides of a well-isolated turning point, and expressions for the wave function in… -- 2.4.1 Symmetry relations and estimates of the F-matrix elements -- 2.4.2 Parameterization of the matrix… -- 2.4.2.1 Changes of Alpha, Beta and Gamma when x1 moves in the classically forbidden region -- 2.4.2.2 Changes of Alpha, Beta and Gamma when x2 moves in the classically allowed region -- 2.4.2.3 Limiting values of Alpha, Beta and Gamma -- 2.4.3 Wave function on opposite sides of a well-isolated turning point. |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 2.4.4 Power and limitation of the parameterization method -- 2.5 Phase-integral connection formulas for a real, smooth, single-hump potential barrier -- 2.5.1 Exact expressions for the wave function on both sides of the barrier -- 2.5.2 Phase-integral connection formulas for a real barrier -- 2.5.2.1 Wave function given as an outgoing wave to the left of the barrier -- 2.5.2.2 Wave function given as a standing wave to the left of the barrier -- 3 Problems with solutions -- 3.1 Base function for the radial Schrödinger equation when the physical potential has at the most a Coulomb singularity at… -- 3.2 Base function and wave function close to the origin when the physical potential is repulsive and strongly singular at… -- 3.3 Reflectionless potential -- 3.4 Stokes and anti-Stokes lines -- 3.5 Properties of the phase-integral approximation along an anti-Stokes line -- 3.6 Properties of the phase-integral approximation along a path on which the absolute value of exp[iw(z)] is monotonic in… -- 3.7 Determination of the Stokes constants associated with the three anti-Stokes lines that emerge from a well-isolated… -- 3.8 Connection formula for tracing a phase-integral wave function from a Stokes line emerging from a simple transition zero… -- 3.9 Connection formula for tracing a phase-integral wave function from an anti-Stokes line emerging from a simple transition… -- 3.10 Connection formula for tracing a phase-integral wave function from a classically forbidden to a classically allowed… -- 3.11 One-directional nature of the connection formula for tracing a phase-integral wave function from a classically… -- 3.12 Connection formulas for tracing a phase-integral wave function from a classically allowed to a classically forbidden… -- 3.13 One-directional nature of the connection formulas for tracing a phase-integral wave function from a classically allowed…. |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 3.14 Value at the turning point of the wave function associated with the connection formula for tracing a phase-integral… -- 3.15 Value at the turning point of the wave function associated with a connection formula for tracing the phase-integral… -- 3.16 Illustration of the accuracy of the approximate formulas for the value of the wave function at a turning point -- 3.17 Expressions for the a-coefficients associated with the Airy functions -- 3.18 Expressions for the parameters Alpha, Beta, and Gamma when… -- 3.19 Solutions of the Airy differential equation that at a fixed point on one side of the turning point are represented by a… -- 3.20 Connection formulas and their one-directional nature demonstrated for the Airy differential equation -- 3.21 Dependence of the phase of the wave function in a classically allowed region on the value of the logarithmic derivative… -- 3.22 Phase of the wave function in the classically allowed regions adjacent to a real, symmetric potential barrier, when the… -- 3.23 Eigenvalue problem for a quantal particle in a broad, symmetric potential well between two symmetric potential barriers… -- 3.24 Dependence of the phase of the wave function in a classically allowed region on the position of the point x1 in an… -- 3.25 Phase-shift formula -- 3.26 Distance between near-lying energy levels in different types of physical systems, expressed either in terms of the… -- 3.27 Arbitrary-order quantization condition for a particle in a single-well potential, derived on the assumption that the… -- 3.28 Arbitrary-order quantization condition for a particle in a single-well potential, derived without the assumption that… -- 3.29 Displacement of the energy levels due to compression of an atom (simple treatment) -- 3.30 Displacement of the energy levels due to compression of an atom (alternative treatment). |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 3.31 Quantization condition for a particle in a smooth potential well, limited on one side by an impenetrable wall and on… -- 3.32 Energy spectrum of a non-relativistic particle in a potential proportional to… -- 3.33 Determination of a one-dimensional, smooth, single-well potential from the energy spectrum of the bound states -- 3.34 Determination of a radial, smooth, single-well potential from the energy spectrum of the bound states -- 3.35 Determination of the radial, single-well potential, when the energy eigenvalues are… -- 3.36 Exact formula for the normalization integral for the wave function pertaining to a bound state of a particle in a… -- 3.37 Phase-integral formula for the normalized radial wave function pertaining to a bound state of a particle in a radial… -- 3.38 Radial wave function psi(z) for an s-electron in a classically allowed region containing the origin, when the… -- 3.39 Quantization condition, and value of the normalized wave function at the origin expressed in terms of the level density… -- 3.40 Expectation value of an unspecified function f(z) for a non-relativistic particle in a bound state -- 3.41 Some cases in which the phase-integral expectation value formula yields the expectation value exactly in the… -- 3.42 Expectation value of the kinetic energy of a non-relativistic particle in a bound state. Verification of the virial… -- 3.43 Phase-integral calculation of quantal matrix elements -- 3.44 Connection formula for a complex potential barrier -- 3.45 Connection formula for a real, single-hump potential barrier -- 3.46 Energy levels of a particle in a smooth double-well potential, when no symmetry requirement is imposed -- 3.47 Energy levels of a particle in a smooth, symmetric, double-well potential. |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 3.48 Determination of the quasi-stationary energy levels of a particle in a radial potential with a thick single-hump barrier -- 3.49 Transmission coefficient for a particle penetrating a real single-hump potential barrier -- 3.50 Transmission coefficient for a particle penetrating a real, symmetric, superdense double-hump potential barrier -- References -- Author index -- Subject index. |

520 ## - SUMMARY, ETC. | |

Summary, etc. | A mathematical approximation method important for many branches of theoretical physics, applied mathematics and engineering. |

588 ## - SOURCE OF DESCRIPTION NOTE | |

Source of description note | Description based on publisher supplied metadata and other sources. |

590 ## - LOCAL NOTE (RLIN) | |

Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name entry element | WKB approximation. |

9 (RLIN) | 52517 |

655 #4 - INDEX TERM--GENRE/FORM | |

Genre/form data or focus term | Electronic books. |

9 (RLIN) | 52518 |

700 1# - ADDED ENTRY--PERSONAL NAME | |

Personal name | Fröman, Per Olof. |

9 (RLIN) | 52519 |

776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |

Relationship information | Print version: |

Main entry heading | Fröman, Nanny |

Title | Physical Problems Solved by the Phase-Integral Method |

Place, publisher, and date of publication | Cambridge : Cambridge University Press,c2002 |

International Standard Book Number | 9780521812092 |

797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |

Corporate name or jurisdiction name as entry element | ProQuest (Firm) |

856 40 - ELECTRONIC LOCATION AND ACCESS | |

Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/thebc/detail.action?docID=202083">https://ebookcentral.proquest.com/lib/thebc/detail.action?docID=202083</a> |

Public note | Click to View |

887 ## - NON-MARC INFORMATION FIELD | |

Content of non-MARC field | EBK |

942 ## - ADDED ENTRY ELEMENTS (KOHA) | |

Koha item type | Ebrary |

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