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.
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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