Quantum particle in a random medium

We describe the behavior of a quantum particle in a random medium using the Green's function in the functional integral representation and propose methods for evaluating it. We calculate the localization length in the case of motion in a disordered medium and in a medium described by a random Gaussian-type potential. We consider the motion of the quantum particle in the quantized-field vacuum and show the difference between the relativistic and nonrelativistic approaches.