Meanvalue picture and ‘equivalent potential’ for a stochastic gluon background field

The main results (energy spectrum and the wave function at the origin) of a model with a stochastic gluon background field — the model of Dosch and Marquard — are alternatively achieved by the so-called meanvalue picture. In this approach it is not necessary to know the details of the stochastic process, therefore the formulas in this meanvalue picture emerge very simply. A local ‘equivalent potential’ to the stochastic process is deduced which reproduces with high accuracy the results of Dosch and Marquard for all values of the gluon correlation time. At last we compare this ‘equivalent potential’ with the well-known linear potential of Eichten et al.