A new formalism is presented for high-energy analysis of the Green function for Fokker-Planck and Schr\"odinger equations in one dimension. Formulas for the asymptotic expansion in powers of the inverse wave number are derived, and conditions for the validity of the expansion are studied through the analysis of the remainder term. The short-time expansion of the Green function is also discussed.
Low-energy asymptotic expansion of the Green function for one-dimensional Fokker-Planck and Schrödinger equations
Solutions of Helmholtz and Schrödinger Equations with Side Condition and Nonregular Separation of Variables
Accurate calculation of Green functions on the d-dimensional hypercubic lattice
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