Complex Potential Of The Tunneling Time

The problem of wave tunneling through a quantum-mechanical barrier had been brought out for many years, in which the probability and time of tunneling was probed into by scholars. Nowadays, the tunneling time of particles transmitting single or multiple quantum barriers has drawn much attention again, especially with the advent of techniques for the fabrication of semiconductor tunneling devices, such as single-electron tunneling transistors, resonant tunneling diodes, quantum cascade lasers, and resonant photo detectors. But it is well-known that velocity and momentum are not confirmed simultaneously, because of the principle of the uncertainty relation, the time is not observed. Therefore, the study of the particles tunneling time transmitting the quantum barriers is very significant to the semiconductor tunneling devices development.The density of probability is commonly not conservation in practice, so that the complex potential taken in atomic nucleus physics and the scattering theory, is introduced into the paper to describe the tunneling time. It studied several representative potentials by analytical methods of the phase time, including single complex Diracδpotential, double complex Diracδpotentials and rectangular complex potential, and analyzed visually with the aid of Matlab and Origin software.The phase time T_τis inverse ratio of the particles energy E ,the real of complex potential Re is more effective than the imaginary of complex potential Im , which all emerge when the particles transmit the single complex Diracδpotential; T_τappearing damping attenuation with the changing of E , T_τcomplete increasing with the distance of double complex Diracδpotential a , Re more effective than Im , and T_τappearing a minimum with the increasing of Im , which emerge when the particles transmit the double complex Diracδpotential; T_τcomplete increasing with the increasing of E, T_τappearing a maximum with the changing of E, T_τcomplete increasing with barrier width of rectangular complex potential a, Re more effective than Im if E is low, contrarily, Im more effective than Re if E high, which all emerge when the particles transmit the rectangular complex potential.