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Physical Problems Solved by the Phase-Integral Method Book

Physical Problems Solved by the Phase-Integral Method
Physical Problems Solved by the Phase-Integral Method, , Physical Problems Solved by the Phase-Integral Method has a rating of 3 stars
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  • Physical Problems Solved by the Phase-Integral Method
  • Written by author Nanny Froman
  • Published by Cambridge University Press, June 2002
  • A mathematical approximation method important for many branches of theoretical physics, applied mathematics and engineering. Booknews This book serves as an introduction to an approximation method for the analysis and solution of problems
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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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