About 25 years ago, the author found that by a dissipative coupling, the penetrability of a potential barrier is increased, not decreased as it was believed before. A dissipative coupling includes two physical effects: (1) an increase of the action of the system, which leads to a decrease of the barrier penetrability, as it was shown by Caldeira and Leggett, and (2) additional transitions resulting from the dissipative terms of Lindblads master equation, which lead to a penetrability decrease. With the tunneling and momentum operators in Lindblads dissipative term, the author found a good agreement of the theoretical results with the experimental spectra of some cold fission modes. However, later, important theoretical progresses appeared. First of all, he found Lindblads theory very unsatisfactory, including a large number of unspecified parameters. Using a method of Ford, Lewis, and O2Connell for the reduced dynamics, he obtained a quantum master equation with explicit, analytical parameters, depending on the dissipative potential matrix elements, densities of the environment states, and occupation probabilities of these states, for a complex environment of other fermions, bosons, and a free electromagnetic field. More than that, he found that a particle wave function includes the Lagrangian in the time dependent phase of a particle wave function, instead of the Hamiltonian of the conventional Schrdinger equation. In this case, the wave equation includes an additional term depending on momentum and velocity, and the penetrability of a potential barrier takes an explicit form, depending on physical characteristics, velocity, and spin.