est principal maxima are partitioned from each other by N − 2 = 5 subsidiary maxima. wave equation [13]. Superposition of the Gaus- sian wave packets from the slit grating can be represented by linear combination of orthogonal functions also. So, solutions of the Schr¨ odinger wave equation underlie this superposition as well. Madelung and next Bohm had shown [14– 16], that the Schr¨ odinger equation can be re- duced to two coupled equations, the both for real-valued functions. With the purpose of the following analysis of the interference effect we remind these equations. Almost at the same time with publication of the epochal article of Schr¨ odinger [13], Madelung published his article entitled ”Quantum theory in hydrodynamic form” [14]. In this article Madelung found a deep analogy of behavior of the quantum system described by a wave func- tion with the behavior of ideal liquid. The first step is that, the complex-valued wave function can be represented by sum of the functions, each is real-valued function. One of this real- valued function reduces conditionally to a rule for finding velocity of a liquid outflow. The other function gives conservation of density of such a quantum liquid. Equations, describing these two manifestations of the quantum liquid, are well known the Hamilton-Jacobi equation and the continuity equation mentioned in Introduc- tion. They are Eqs. (2) and (4). A main dif- ference exists, however. The difference is that the HJ-equation has an extra term, so-called the quantum potential [15–17]. These renewed equations read Fig. 6 shows diffraction from N = 7 slits grat- ing in the far-field zone, distance z = 10 $^{7}$z$_{T}$ = 1 m. It is seen, that the principal maxima are partitioned from each other by N − 2 = 5 sub- sidiary maxima. The curve depicted by red cir- cles relates to the probability density, that is calculated by Eqs. (22)-(23). Intensity (24) is drawn by solid curve. The both curves drawn in the figure give a good agreement. The dotted curve represents envelope I$_{0}$ ( x, z ) · N $^{2}$. Majority of known in physics functions are representable by linear combination of orthog- onal functions, that are solutions of Schr¨ odinger is Hamiltonian of the quantum system, where U ( ⃗ q ) is a potential energy. The term Q ( ⃗ q , ⃗ p ; t ) is the quantum potential IV. MADELUNG-BOHMIAN INSIGHT FIG. 5: Diffraction in the far-field zone by scattering thermal neutrons ( λ = 0 . 5 nm) on N = 7 slits grating. Directions of principal and subsidiary maxima are pointed out by red and blue arrows, respectively. Distance between slits d = 10 λ , width of slits a = 2 λ , effective width σ ≈ 0 . 534 a . FIG. 6: Diffraction in the far-field zone from N = 7 slits grating, distance z = 1 m. Circles relate to the probability density calculated by Eqs. (22)-(23). Intensity (24) is drawn by solid curve. Dotted curve draws envelope I$_{0}$ ( x, z ) · N $^{2}$. Here − ∂S ∂ t = H ( ⃗ q , ⃗ p ; t ) + Q ( ⃗ q , ⃗ p ; t ) , (27) ∂ρ ∂ t + ( ⃗ v ∇ ρ ) = 0 . (28) H ( ⃗ q , ⃗ p ; t ) = ( ∇ S ) 2 2 m + U ( ⃗ q ) (29) Q ( ⃗ q , ⃗ p ; t ) = − ¯ h 2 2 m$^{[}$ ∇ $^{2}$ρ 2 ρ −$^{(}$ ∇ ρ 2 ρ$^{)}$$^{2}$$^{]}$ (30) 8 4z$_{T}$ 8z$_{T}$ 12z$_{T}$ 16z$_{T}$ 20z$_{T}$ 24z$_{T}$ slits { -0.1 0 0.1 0 2 4 p(x,z) x , m