Physical Problems Solved by the Phase-Integral Method

图书简介

This book covers a mathematical approximation method of central importance to many branches of theoretical physics, applied mathematics and engineering. Written with practical needs in mind, with 50 solved problems to demonstrate the applications of the method and the concepts involved. Ideal as an introduction for graduates and a reference for researchers.

Part I. Historical Survey: 1. History of an approximation method of wide importance in various branches of physics; Part II. Description of the Phase-Integral Method: 2. Form of the wave function and the q-equation; 3. Phase-integral approximation generated from an unspecified base function; 4. F-matrix method; 5. F-matrix connecting points on opposite sides of a well isolated turning point, and expressions for the wave function in these regions; 6. Phase-integral connection formulas for a real, smooth, single-hump potential barrier; Part III. Problems With Solutions: 1. Determination of a convenient base function; 2. Determination of a phase-integral function satisfying the Schrödinger equation exactly; 3. Properties of the phase-integral approximation along certain paths; 4. Stokes constants and connection formulas; 5. Airy’s differential equation; 6. Change of phase of the wave function in a classically allowed region due to the change of a boundary condition imposed in an adjacent classically forbidden region; 7. Phase shift; 8. Nearlying energy levels; 9. Quantization conditions; 10. Determination of the potential from the energy spectrum; 11. Formulas for the normalization integral, not involving the wave function; 12. Potential with a strong attractive Coulomb singularity at the origin; 13. Formulas for expectation values and matrix elements, not involving the wave function; 14. Potential barriers; References.

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Physical Problems Solved by the Phase-Integral Method 相位计分方法解决的物理问题 理论物理学

Physical Problems Solved by the Phase-Integral Method

相位计分方法解决的物理问题
理论物理学