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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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