Table of Contents

A brief history of quantum tunnelling; some basic questions concerning quantum tunnelling; semi-classical approximations and the Bohr-Sommerfeld method; Gamow's theory, complex eigenvalues and the time-dependence of the wave function; simple solvable problems and tunnelling in symmetric and asymmetric wells; classical description of tunnelling; time-dependent and non-local potential barriers; decay width and the scattering theory; variable reflection amplitude and multi-channel tunnelling; path integral method in quantum tunnelling; Heisenberg's equations of motion and the Wigner distribution function; complex scaling and dilatation transformation for calculation of the decay width; multidimensional quantum tunnelling; time-delay, reflection time, dwell, phase and minimum tunnelling time; tunnelling of a system with internal degrees of freedom; motion of a particle in a space bounded by a surface of revolution; relativistic formulation of quantum tunnelling; inverse problems of quantum tunnelling; examples from atomic, molecular, nuclear and condensed matter physics.