Interpretation of a Schrödinger-like equation derived from a non-Markovian process.

Abstract

Hydrodynamical equations for the probability density \ensuremath{\rho} and the local velocity v of a non-Markovian stochastic process have been recently obtained. The corresponding complex equation in terms of the wave function \ensuremath{\psi} coincides with the Schr\odinger equation if the first-order terms only are retained. The second-order terms vanish and the third-order terms could be considered as QED-type corrections. To obtain the coefficient ${\mathit{D}}_{4}$ of the third-order term the probability density \ensuremath{\rho} for a free particle is obtained by stochastic electrodynamics. This solution is substituted in the new complex equation, thus obtaining ${\mathit{D}}_{4}$. By this coefficient the calculation of the Lyman-\ensuremath{\alpha} wavelength is in agreement with the best direct measurements for the transition 2P\ensuremath{\rightarrow}1S. The 1S displacement is 1% of the QED value for the Lamb shift. It is suggested how the new negative contribution could be the difference between the (1+0.01) QED value for the 3S state and the corresponding experimental value, which is 20% less than that given by QED.