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This book provides a thorough introduction to one of the most efficient approximation methods for the analysis and solution of problems in theoretical physics and applied mathematics. It is written with practical needs in mind and contains a discussion of 50 problems with solutions, of varying degrees of difficulty. The problems are taken from quantum mechanics, but the method has important applications in any field of science involving second order ordinary differential equations. The power of the asymptotic solution of second order differential equations is demonstrated, and in each case the authors clearly indicate which concepts and results of the general theory are needed to solve a particular problem. This book will be ideal as a manual for users of the phase-integral method, as well as a valuable reference text for experienced research workers and graduate students.
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This book treats the Stark effect of a hydrogenic atom or ion in a homogeneous electric field. It begins with a thorough review of previous work in this field since 1926. After the Schrödinger equation has been separated with respect to time dependence, centre of mass motion and internal motion, followed by a discussion of its eigenfunctions, the exact development in time of the probability amplitude for a decaying state is obtained by means of a formula analogous to the Fock-Krylov theorem. From this formula one obtains by means of the phase-integral approximation generated from a particular
Stark effect. --- Optical spectroscopy. --- Quantum theory. --- Schrödinger equation. --- Equation, Schrödinger --- Schrödinger wave equation --- Differential equations, Partial --- Particles (Nuclear physics) --- Wave mechanics --- WKB approximation --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Spectroscopy, Optical --- Visible spectroscopy --- Spectrum analysis --- Electrooptics --- Spectral line broadening --- Schrodinger equation.
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