Quantum theory of tunneling

A comprehensive introduction to the theoretical foundations of quantum tunnelling, stressing the basic physics underlying the applications. The topics addressed include exponential and non-exponential decay processes and the application of scattering theory to tunnelling problems. In addition to the Schrodinger 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 tunnelling of particles with internal degrees of freedom are also considered. Furthermore, advances concerning time delay and tunnelling times and some of the problems associated with their measurement are also discussed. Finally, some examples of tunnelling in atomic, molecular, nuclear and condensed matter physics are presented.

A brief history of quantum tunneling -- Some basic questions concerning quantum tunneling -- Semi-classical approximations -- Generalization of the Bohr-Sommerfeld quantization rule and its application to quantum tunneling -- Gamow's theory, complex eigenvalues, and the wave function of a decaying state -- Simple solvable problems -- Tunneling in confining symmetric and asymmetric double-wells -- A classical description of tunneling -- Tunneling in time-dependent barriers -- Decay width and the scattering theory -- The method of variable reflection amplitude applied to solve multichannel tunneling problems -- Path integral and its semi-classical approximation in quantum tunneling -- Heisenberg's equations of motion for tunneling -- Wigner distribution function in quantum tunneling -- Complex scaling and dilatation transformation applied to the calculation of the decay width -- Multidimensional quantum tunneling -- Group and signal velocities -- Time-delay, reflection time operator and minimum tunneling time -- More about tunneling time -- Tunneling of a system with internal degrees of freedom -- Motion of a particle in a space bounded by a surface of revolution -- Relativistic for…