Quasi-Classical Expansion of Schrödinger Equation and Conformal Field Theory

Supervisor

Prof. Vladimir Bazhanov Phone: 6125 5500

The method of Baxter's commuting operators and functional relations is a powerful method in the theory of integrable quantum systems, which covers both solvable lattice models and models of continuous quantum field theory. The most recent developments in this field based on a remarkable connection between the conformal field theory and the spectral theory of ordinary differential equations, in particular, the Schrödinger equation. It turns out that the eigenvalues of the Baxter's commuting operators coincide with monodromy coefficients of certain differential equations, while the quasi-classical approximation for these equations corresponds to the low-temperature limit in associated physical systems. The aim of the project is to develop a computer program for systematic analytic calculation of the quasi-classical expansion for the Schrödinger equation.