D.S.F. Crothers (auth.)038774312X, 9780387743127, 9780387743134
This text concerns ‘semiclassical’ within various meanings. These include the familiar JWKB approximation and its phase-integral generalizations in Chapter 2 to two and four transition points with or without one or two poles: by corollary, crossing and non-crossing nonadiabatic collision theory. Above and below threshold Wannier ionization is covered in Chapter 3 where the large parameters are the inverses of the variation of the hyperspherical angles from their ridge values. The more familiar impact parameter treatment, in which the possibly relativistic heavy-particle relative motion is treated classically and the electrons quantally, is well covered in Chapter 4. Diffusion in solids and liquids is described in Chapter 5 where typically the large parameter is the height of the barrier which is overcome by thermal agitation. Hypergeometric functions are introduced in Chapter 1 and Mittag-Leffler functions in Appendix B.
Table of contents :
Front Matter….Pages I-XI
Mathematics for the Semiclassicist….Pages 1-20
Semiclassical Phase Integrals….Pages 21-91
Semiclassical Method for Hyperspherical Coordinate Systems….Pages 93-138
Ion–Atom Collisions….Pages 139-241
Diffusion in Liquids and Solids….Pages 243-303
Back Matter….Pages 305-342
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