QUANTUM TUNNELING IN MEDIUMS WITH LINEAR AND NONLINEAR DISSIPATION

Abstract

We have applied the method of integration of the Heisenberg equation of motion proposed by Bender and Dunne, and M. Kamella and M. Razavy to the potential V(q) = v q - µ q with linear and nonlinear dissipation. We concentrate our calculations on the evolution of basis set of Weyl Ordered Operators and calculate the mean position , velocity , the commutation relation [q, p], and the energy of particle. According to our results, the particle which is confined in the well at t= 0, has some oscillations before tunneling. If dissipation is lproportional to velocity it inhibits tunneling but when it is quadric in velocity it facilitates tunneling. Thus, we can continue our cdculation easily for every power of velocity