This book provides a comprehensive introduction to the theoretical foundations of quantum tunneling, stressing the basic physics underlying the applications. The topics addressed include exponential and nonexponential decay processes and the application of scattering theory to tunneling problems. In addition to the Schrödinger equation approach, the path integral, Heisenberg's equations and the phase space method are all used to study the motion of a particle under the barrier. Extensions to the multidimensional cases and tunneling of particles with internal degrees of freedom are also considered. Furthermore, recent advances concerning time delay and tunneling times and some of the problems associated with their measurement are also discussed. Finally, some examples of tunneling in atomic, molecular, nuclear and condensed matter physics are presented.
Inhaltsverzeichnis
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.
