Observing Nonclassical Paths by Measuring Bohmian Velocities in Multi-Slit Interferometer with Electron

Superposition principle of wave function in multi-slit interference experiment has been widely accepted by many quantum mechanics textbooks, however the expression ${psi _{AB}} = {psi _A} + {psi _B}$ does not strictly hold. The non-classical paths in Feynman path integral provide an explanation to the multi-path interference effect, and can be used to quantitatively analyse the multi-slit interference effect. In this work, we apply quantities in Bohmian mechanics to the measurement of multi-order interference by analysing the contribution of non-classical paths to Bohmian velocity in electronu0027s multi-slit interferometer. The result shows that the non-classical paths effect will cause a relative deviation of $10^{-3}$ in electronu0027s Bohmian velocity, which is observable by doing weak measurement similar to previous work.