Results of work at Tulane University with M. Herman

Preliminary estimations
Finding the unitary matrix A(x, Delta x) I. Differential equation for the matrix A II. Approximate solutions III. Equations for phase functions IV. Uncoupling the set of differential equations A. Separation of the function phi₀ B. Eliminating the function phi₊ IV. Uncoupling differential equations (31) and (32) V. Expansions on powers of Delta x A. Accuracy of small-coupling approximation B. Accuracy of small-Delta x approximation	PDF file TeX file
Derivation of functions tau and rho from conditions of unitarity I. Relationship between functions tau and rho and the couplong eta II. A similar relationship, but for transition 2 -> 1 III. Conservation of flux IV. Finding tau and rho	PDF file TeX file
Uniform semiclassical approximation for two surfaces I. Definitions II. Zero-order term II. Zero-order term III. Testing zero-order term IV. First-order wave function	PDF file TeX file
Examples of two-level potentials: primitive semiclassical vs. uniform semiclassical approximation	Table with links
Study of two-dimensional potentials, in progress	Table with links